Update August 31, 2022
Can firearms be shipped through the U.S. Mail (USPS)?
Some firearms can be shipped through the U.S. mail. Whether certain firearms can be shipped through the U.S. mail depends on what type of firearms they are. Simply, long guns: yes; handguns: no.
Handguns are not allowed to be mailed through USPS. See 18 U.S.C. §§1715, 922(a)(3), 922(a)(5), and 922(a)(2)(A). Rather, handguns must be shipped using a common or contract carrier (e.g., UPS or FedEx).
Shipping handguns and other firearms through a common or contract carrier
Under federal law, a non-licensed individual may ship a firearm (including a handgun) by a common or contract carrier (e.g., UPS or FedEx – unfortunately, neither UPS or FedEx will allow a private individual to ship using their services any longer.
Please check with the carrier of your choice regarding their firearm shipping policy) to a resident of his or her own state, or to a licensed individual (FFL) in another state. However, it is illegal to ship any firearm to a non-FFL in another state. The carrier must be notified that the shipment contains a firearm, however, carriers are prohibited from requiring any identifying marks on the package which may be used to identify the contents as containing a firearm. See 18 U.S.C. §§922(a)(2)(A), 922(a)(3), 922(a)(5), 922(e), 27 CFR 478.31 and 478.30.
I think you're confused, and I don't want to get the OP's ad off on a bunny trail, but handguns
can be shipped USPS by an FFL. Maybe this is what you're thinking about-
May a nonlicensee ship a firearm through the U.S. Postal Service? Handguns are not mailable. A common or contract carrier must be used to ship a handgun. This is in reference to non-licensees, NOT licensed dealers.
[18 U.S.C. 1715, 922(a)(5) and 922 (a)(2)(A); 27 CFR 478.31]
Click the link I provided from the ATF and read. Also read USPS Publication 52; 432.23.