You don't need a copy of the receivers FFL to ship but how else are you going to make sure the person really does have a valid FFL? Unless it's going back to the manufacturer, 1st make sure the other persons FFL will even receive from a private party (a lot will not) then make sure you get a signed in ink copy of the receivers FFL then go to the ATF website to verify the persons license is still valid. Won't work with C&R licenses but all other it will. My understanding from UPS is it up to the manager at the center if they will accept. Kinko's can't take them only the main office. Make sure you insure it for every penny and have bill of sale and receipts to back it up. This is from someone who had a G17 stolen from Fed-Ex custody then had a hell'uva time getting them to pay off full value. BTW It has since been recovered and was used in a crime appx 3 hours from my house. It possibly has a body on it now.
Print out the instructions from either Fed-Ex or UPS's web site & take them with you. FFL holders can ship by post office a lot cheaper for you if yours will. Even if he charges you $30.00 to ship it's still cheaper than Fed-Ex at $50-125