Quoted from a knowledgeable guy up above...
" The image posted by Jur is perfect. If the end of the smooth barrel is lined up with the end of the axle 99% of the problems I see are solved. Further than that the internals are worn/broken but this is very uncommon being honest. "
There are many shops in the US that do not carry or know how to service 3 speed bikes. I owned a shop for 30+ years and never sold a 3 speed. The last 3 speed I had was when I was 10 years old. It is not surprizing at all to me that the shop that sold this gentleman a Brompton did not understand 3 speed adjustment.