Have the customer send you copies of the invoices, cross reference them with your documentation and if they match, just refund him the money and tell him to toss the parts in the trash.
You'll never make him happy and never get a straight answer.
I have a home base business where I restore Bosch ignition distributors from the 50s and 60s. I sold one to a person and a month later I get a email from him stating it didn't work right, he sent to someone else to repair and said it was junk and sold him one of his. I asked the original customer why he didn't contact me and never got a straight answer. I told the original customer to send it back to me and I would refund every cent it cost him including shipping both ways. When I got it back the person he sent it to messed with it so I rebuilt it again. 3 days later I sold it to a local customer who drive to my house and I installed it. it ran perfectly and 5 years later I still know the local guy and it works flawlessly. I lost $80 between the shipping and tune up parts I couldn't sell as new, but I never heard from the original customer again so it was money well spent.
My point is you can't argue with stupid, so don't try.