As doubleA said, a person may send a firearm (hand gun or long gun) to the manufacturer or a licensed gunsmith with out having to go through an FFL holder. You do not need a copy of the FFL to put into the case with the firearm.
A long gun may be shipped ground through the post office, UPS, Fed-X or any other private carrier.
A hand gun must be shipped over night and must go private carrier. The post office will not ship hand guns.
You must go directly to the actual USPS, UPS or Fed-X hub to ship a firearm. The postal carrier nor the UPS/Fed-X "stores" will ship a firearm.