It's worse than that. You will also need 2 anti-rotation washers to mate the axle flats on the hub to the dropouts on the Harding. These might have to be custom made if regular Sturmey Archer washers don't work. Looks like you need axle nuts too and I don't see a fulcrum clip in the photo. You would need a fulcrum clip the correct size to fit your top tube. Maybe someone here who has done this sort of conversion could help with the anti-rotation washer issue. I've never done this, so I don't know.
anti rotation washers

This picture is everything in the box.
I am certiantly missing the lock nuts. My LBS does sell new stock SA parts but I'm unsure if they would work for this project.
I'm starting to wonder if I should just start with a simpler 3 speed conversion and save this 4 speed hub for when I have more parts and experience at my disposal.
Edit:
I mean to say a 3 speed, or even a 5 speed conversion would be more cost effective. Maybe not simpler, but cheaper and easier to get a hold of parts for.
https://cimg1.ibsrv.net/gimg/bikefor...1dee7d5e01.jpg

Lots of people here have done this sort of project. It would be good to hear what they have to say. I wish I could be more helpful. But it is true, you are missing parts. Along with whatever cog you choose, It looks like you will also need 2 spacer rings and the circlip that holds the cog. I know, the list keeps getting longer, but I think that's about everything and it is a worthy project.

You have been immensely helpful BigChief!
I may post a new thread and see if I can bring in any of those 4 speeders.
I do still want to do this. It seems I'm missing the smaller bits and if I can find those parts at a not insane markup I'm still in.

Put the oil in after the wheel is built up, otherwise its a pain to make the wheel!
The shifter really isn't any different- to understand this fact better, if you use a 3 speed shifter on a 4 speed hub, the only difference is you can't access the lower gear, so the 4 speed will then act exactly like a three speed. So you can use the universal or dedicated shifter with no worries.

Really, and seriously, unless you can get smaller chainrings for the Lambert crankset, the problem you'll run into is that the gears will be way too high, unless you are a serious masher, keeping in mind that 27" wheels also contribute to a higher gear. I run a 46 on the front and a 19 on the rear of my Humber Sports, and its set up with 26" wheels. High is plenty high and I'm thinking about a 21 on the rear so low will be appropriately lower than my 3-speeds and high will still be higher.

Robin Hood
Since replacing a warped crank on the left side, my Robin Hood has turned out to be a very pleasant riding bike.
https://cimg9.ibsrv.net/gimg/bikefor...d54c1a7488.jpg
I did a 20 mile round trip the other day with no issues.
I have added a new set of MKS pedals and this weekend
may swap out the rear cog and install a new chain.
Current saddle is a vintage Wrights,
https://cimg4.ibsrv.net/gimg/bikefor...3954807a70.jpg

The FW requires the long-throw four-speed shifter. Look for a shifter that either says "3 or 4 speed" or has the "4-speed" right on the front. A standard AW three speed shifter will leave you with a reduced-ratio hub that is missing its bottom gear.

You'll need two long-type axle nuts/sleeves. The diagram in the box shows them. The drive-side is a standard AW-type nut/sleeve combo where the indicator/shifter spindle comes out. The non-drive side is similar, but slightly different in that the center section is more open. This non-drive side combo protects shifter spindle that pokes out of the non-drive side of the axle. It is possible to use a standard AW drive-side nut/sleeve and open the center up a bit with a Dremel or file. This allows the non-drive shifter rod to move in and out of the axle while protecting that rod.

You'll need a basic set of spacers so you can center the wheel in the frame.

You'll need keyed spacers to lock the axle in the rear dropout. These are "anti-rotation washers". Buy Sturmey-made anti-rotation spacers. The FW should work with AW-type spacers. If your rear drop is different from Raleigh pattern, you'll need to grind and file the Sturmey type to fit. If the Sturmey type are too small stock, you'll need to make your own from another brand's type of this spacer (Shimano maybe?).

You'll need everything the AW needs for transmission - fulcrum clamp and ferrule; pulley (looks like you have it); cable. A generic Sunlite AW cable can work, or you can make one using a cable blank and a Bell Systems crimper.

If you choose to re-grease the bearings in the FW, do so without opening up the hub - just pull the cones. The FW and S5 have to be properly tooth timed, which is something you don't have to worry about on the AW. It's not a big deal, but better left alone if all you're doing is re-greasing outer bearings.

Sturmey archer anti-rotation washers are available to fit the narrow dropout openings on something like a Sports as well as the normal 10mm (or a tad larger to fit a 10mm axle) opening of standard bike frame dropouts. I bought some of these from Niagara, which had a selection of SA stuff available. But, who knows if Niagara is still viable? SJS in UK has probably the most complete selection of stuff for SA applications but shipping costs are a problem unless you want a Carradice bag or something to amortise out the costs.

edit some more:

Here's the anti-rotation washer that you need for your Harding:Washer

edit: I recently bought some 25.4 mm fulcrum clips from an Ebay seller at a reasonable price. 25.4 mm is for a normal old TT where as old dt was 28.6 mm. Believe the seller was Wheel and Sprocket which may be a long term Wisconsin outfit -- appear to ship from Appleton.

Here's a nice Carradice bag you can buy at the same time you buy your washers. Carry your lunch and lunch for all your friends, too. !And some Barley

Thanks
The distortion was minimal but enough to throw it off.
It's got a very smooth and quiet 63 hub.
https://cimg7.ibsrv.net/gimg/bikefor...9d12a8fc21.jpg
Only small issue is the replacement crank is square cut as opposed to rounded off, as on the drive side.
https://cimg4.ibsrv.net/gimg/bikefor...a5603aec17.jpg
It seems that squirrels have little to no interest in British 3 Speeds.
https://cimg9.ibsrv.net/gimg/bikefor...24b50c973f.jpg

You sir are a gentleman and a scholar! Thank you for this.

would this cable work?
https://www.sjscycles.co.uk/cables/fibrax-complete-sturmey-archer-3-speed-gear-cable/?geoc=US
I can order a decent amount from this site, but the shipping from the UK is expensive so if I can get all or near all the parts I need from here it would most certiantly even out the cost.
the box came with one of the axel nuts but I dont know which one. This site has the standard right hand side but I'm not seeing any for the non-drive side.
oh well 3 out of 4 isn't bad.
I can order the fulcrum, the washers, and potentially the cable as well from them.

More edit:
it looks as though the nut I have is for the non drive side!
The axel can move in and out of the nuts opening. from what you had said if it was the drive side this would not be the case. https://cimg1.ibsrv.net/gimg/bikefor...77a6fedb95.jpg

Thank you too! Links and all!
Shipping is about 16 dollars this way which isn't too insane. But how can I turn down that bag!? Its even on sale!
I'm wondering if I could order all the bits and pieces I'm gonna need from here in one go...

there are sources in the U.S., probably, for everything that you can get from SJS. But, if you look through their website, you might find everything you need and some cool stuff at a good price besides. Don't forget that you get a rebate on the VAT which may or may not be reflected in the prices quoted. I've bought stuff from them several times over the years and have always been satisfied with their service. Their prices on Carradice bags (which are really quite nice) are as good as any I've found.

That's not the axle moving; it's the indicator rod that moves the clutch inside the hub to select the various gears. Unlike the more common AW hub, the FW (and some SW hubs) uses a two-piece indicator rod:

http://www.os2.dhs.org/~john/two-piece-indicator.jpg

As you note, the FW hubs put the windowed nut on the non-drive side and the gear adjustment is made by setting cable tension to make the end of the rod flush with the axle end.

Although a window on the drive side is unneeded, you can use another windowed nut on the drive side to make a smooth exit path for the chain attached to the indicator rod. Originally, the hub would have come with a non-windowed nut for that side, but those are fairly scarce these days and offer no functional benefit over using a more widely available windowed nut:

http://www.os2.dhs.org/~john/sa-nds-windowed-nut.jpg

Woah okay I gotcha.
So it seems I've lucked out by having the none drive side nut included.
I haven't had any luck finding the non window options as you said they seem to be quite scarce.
Is this a standard aw window style you are referring too?
https://www.sjscycles.co.uk/hub-spares/sturmey-archer-rh-axle-nut-cp-hmn129/?geoc=US

From the sounds of it I think you're better off buying a donor bike for the bits and pieces,
Seriously, they discard these wheels/hubs out back of bike shops all the time.
Complete bikes are often at the side of the road.
Most bike shops have new 3 speed cables @ $8.00-$14.00.
If you ask there's usually a bin of assorted 3 speed parts in
the back somewhere.
You'll pay more for a couple of lock washers + shipping
than for a parts bike.
They're out there.

There are a lot of unwanted stepthroughs out there, but it's too bad this hub didn't come with the complete package. I think a shifter was included originally too. He may need those special anti rotation washers, but having to find a cable,fulcrum clip, cog, circlip, a pair of spacer rings and axle nuts is unfortunate.

https://www.sjscycles.co.uk/images/p...edium/2474.jpg

Yes, that should work just fine.

+1 For parts bike.
I let go of thay rusty 21" 3 speed sports and I'm regretting it now. I got offered twice what I paid and my bike fund was looking paltry. Now it looks like it would cost me the amount I got out of that bike to get the spare parts I could've taken from it haha
I do see a lot of step throughs on the cheap...
does it matter if it's a schwin?
the market here is flooded with schwin step throughs.
My understanding is that as long as the hub is SA the parts will be usable, but I want to check.

Except for Sturmey Archer parts, nothing from a Schwinn is of any use to me, but my hobby is English bikes.

I mean those are the only parts I want Haha
I'm not a particular fan of schwinns. I know they have some supporters but I just dont find them interesting.
I'm just wondering if schwinn actually used sturmey parts. Shifter cables, pulleys, spacers etc.

SA hubs, especially the older ones have top quality plating. Plus, they were sometimes protected by a coat of greasy crud, so it is common to find a totally rusted away bike while the hub cleans up to be in very good condition. That's why you see so many hubs for sale on eBay. Over the years people and mechanics would toss a rotted away wheel but save the perfectly good hub. 20 years ago it was pretty easy to find free English junkers from the 50s and 60s, but they are becoming more rare all the time. These days, roadside junk day finds are mostly Asian bikes from the 90s.

I picked up a ladies bike last year for $20.00. Harvested parts include:
Front and rear brake calipers
Trigger in good shape
Handle bars and stem
Seat post
assorted cable clips
Clean rear hub (cut from rusted rim)
Pair of brake levers
Pair of grips
Most of these parts have migrated over to other projects
or into the parts bin.
https://cimg4.ibsrv.net/gimg/bikefor...14d6a17886.jpg
https://cimg5.ibsrv.net/gimg/bikefor...b281d5c97e.jpg
https://cimg1.ibsrv.net/gimg/bikefor...ff85549506.jpg

wow, your parts are so well organized. At least I recently migrated mine from falling apart cardboard boxes into plastic bins. Good deal at 20 bucks. I see you got a good pair of single bolt levers out of it. Nice. These always come in handy for fixing an otherwise nice mid 70s Raleighs with auto those adjust disasters.

https://cimg6.ibsrv.net/gimg/bikefor...b8b68c5cde.jpg

Obviously, you've spotted the infamous West Village British Bicycle Gang.
They've been terrorizing New York with their incessant demands for
moustache wax and glutten free sustainable snacks
for months now.
Good work.

Raleigh Price Structure
I've often wondered how Raleigh priced their various lines of bikes and what were the differences
in the quality of components that would make a Robin Hood, for example, less expensive than a
a Raleigh branded bike.
I found a "spotty" weld on my Robin Hood.
https://cimg7.ibsrv.net/gimg/bikefor...d581bd374b.jpg
Perhaps, as parts came off the line, seconds (imperfect) were set aside to be used on the lesser brands.
Robin Hoods, Philips, Triumphs, Gliders etc.
Just a thought.

Yes.

Find an old Speedster and take what you need from it, but a Schwinn rim is not the same size as a Raleigh rim so your wheels won't match. Other Schwinns also used Sturmey parts but those models might be more costly to purchase as a parts bike. You can sometimes find Speedsters cheap. My local co-op has a couple that would probably go for $30 each.

Scorchers Be Gone!
A few bikes that were set up as true Scorchers have reverted to a Semi Scorcher state.
Although I really like the look, my back and neck didn't agree.
They'll actually get ridden now.
1961 Superbe.
https://cimg8.ibsrv.net/gimg/bikefor...a4e4eb3d15.jpg
Before.
https://cimg4.ibsrv.net/gimg/bikefor...7565ca215f.jpg
After.
https://cimg9.ibsrv.net/gimg/bikefor...7dc4fa4240.jpg
Heron eye stamp indicates pre 1961.