Form 4457 .....just one of the many Federal forms out there. Yeah, I have always filled them out while traveling with firearms.
Steve

https://help.cbp.gov/app/answers/detail/a_id/323/~/traveling-outside-of-the-u.s.---temporarily-taking-a-firearm%2C-rifle%2C-gun%2C


The only issue I ever had was one of my guns had the same serial# as a gun in the stolen firearms database. A quick check showed my gun to be a rifle and the stolen gun was a pistol. Took maybe 10 minutes to determine that and I was on my way.

Firearms imports, consignments


[Linked Image from i.imgur.com]