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.