Shipping restrictions guidance
Federal law allows "nonlicensees" (people without a federal firearms license) to ship guns, but with certain restrictions. It is your responsibility to know and follow the law in your jurisdiction.
"A nonlicensee may mail a shotgun or rifle ... to a licensee in any State. The Postal Service recommends that long guns be sent by registered mail and that no marking of any kind which would indicate the nature of the contents be placed on the outside of any parcel containing firearms. Handguns are not mailable [via USPS]. A common or contract carrier [like FedEx or UPS] must be used to ship a handgun."
Carriers like FedEx and UPS
"A nonlicensee may ship a firearm by a common or contract carrier ... to a licensee in any State. A common or contract carrier must be used to ship a handgun. In addition, Federal law requires that the carrier be notified that the shipment contains a firearm and prohibits common or contract carriers from requiring or causing any label to be placed on any package indicating that it contains a firearm.
SOURCE: "Firearms - Frequently Asked Questions - Unlicensed Persons" Bureau of Alcohol, Tobacco and Firearms (BATF). Retrieved 3 May 2020. https://www.atf.gov/firearms/firearms-frequently-asked-questions-unlicensed-persons