This page says they do:
But the Service Guide updated on 9/20/2021 says not:
How to Ship Firearms | FedEx
Find out what is required to ship firearms and what licenses you need. Read our guidelines on shipping your gun, including what is prohibited and how to secure your firearm.
www.fedex.com
But the Service Guide updated on 9/20/2021 says not:
Firearms
Only customers holding a Federal Firearms License (FFL) and federal, state, or local government agencies may ship firearms with FedEx. Customers holding an FFL must enter into an approved FedEx Firearms Shipping Compliance Agreement before shipping any firearms with FedEx. For more information, contact your FedEx account executive.On behalf of customers holding an FFL who enter into an approved FedEx Firearms Shipping Compliance Agreement and federal, state, or local government agencies, FedEx Express will transport and deliver firearms, antique firearms, and replica firearms, all as defined by the United States Gun Control Act of 1968, as well as muzzleloaders and black powder firearms (collectively “firearms”). Shipments containing firearms must be sent with the Adult Signature Required Delivery Signature Option.