Sometimes it matters whether you are using UPS directly or an authorized agent of UPS.

Customers ship guns to me all the time without benefit of my having provided my FFL, and I never have any issue with return shipping.

Having said that, last week a customer was having difficulty getting an authorized UPS shipper to send me his gun without proof of my FFL. I offered to fax a copy to the agent, and he said "No, just read me the number and that will be sufficient". Go figure.