A slight addition to Turin's post. I don't think it will be necessary to PROVE ownership in most cases. Register the fact of ownership certainly but PROOF is something else entirely.
If it were me I would email and write to the administrator-once I know who that will be-and state that I xyz am the owner of air rifle abc with serial number 1234567 which was deposited with Litts for service/transmission onwards or whatever it may be. In the case of items without a serial number-such as scopes-a description should be sufficient e.g 'Simmons 3.5-10x50 unboxed in for replacement of smashed rear lens' something that identifies it pretty clearly from ones that are company stock.
'It may be that your sole purpose in life is to serve as a warning to others'.