Following quote is from UPS.com. (I added the bold font.)

"UPS accepts packages containing firearms (as defined by Title 18, Chapter 44, and Title 26, Chapter 53 of the United States Code) and firearm parts that do not constitute firearms as defined by federal law (together, “Firearm Products”) for shipment only as a contractual service and only from Shippers who are licensed importers, licensed manufacturers, licensed dealers, or licensed collectors (as defined in Title 18, Chapter 44 of the United States Code) to authorized recipients, as outlined in the approved UPS agreement for the transportation of Firearm Products."

I did not look up Title 18, Chapter 44, but I assume a licensed collector is someone who has a C&R FFL. If that is true, this is just another reason to get a C&R FFL if you don't already have one.