Brian,
I can never find anything in the USPS DMM for the shipment of firearms. Furthermore, they do not control the transfer of firearms (i.e. they do not ask if you are shipping a firearm). The regulation you are looking for is 27 CFR 478.29a as copied below. As long as you can prove, at the time of receipt, that you are participating in an open season in the state of receipt.
§ 478.29a Acquisition of firearms by
nonresidents.
No person, other than a licensed importer,
licensed manufacturer, licensed
dealer, or licensed collector, who does
not reside in any State shall receive
any firearms unless such receipt is for
lawful sporting purposes.
[T.D. ATF–363, 60 FR 17451, Apr. 6, 1995]
Shoot straight,
Bird
