@RedTag This is not good advice, in my opinion.
A couple years ago, I was coming back to the US after a BC hunt. We cleared US customs in Vancouver, BC. I gave my boarding pass to the CBP officer and he scanned it. Two photos popped up on his screen and he turned it to where I could see it. The photos were of my two checked bags, a duffle bag and a rifle case. The CBP officer pointed to the photo of the rifle case and asked, "What is this?" I told him it was a rifle case with one rifle in it. He then asked to see my Form 4457. I produced it and also mentioned a copy was inside the rifle case. I quickly received the standard "Thank you, have a nice day" response.
My hunting buddy was in another line and it wasn't moving very fast. I waited quite awhile for him to clear. The problem was the two guys ahead of him in line, dressed in camo, didn't have a Form 4457. They were getting invited to the little room and getting their rifles confiscated.
Bottom line: If you are taking a rifle out of the US and plan to bring it back when you return, get a form 4457.