I just got back from my first moose hunt in Canada and there are several things I learned/experienced that I thought might save some other first timers and maybe even veteran international hunters some head aches in the future. Disclaimer- I am not an attorney, travel agent or professional; this is only advice from my recent experience.
What you will need to enter Canada with a "non-restricted firearm"
1. Non Resident firearms declaration form http://www.rcmp-grc.gc.ca/cfp-pcaf/form-formulaire/pdfs/5589-eng.pdf
This is your temporary permit to have a "non restricted" gun in your possession for 60days. Fill out this form ahead of time but DO NOT SIGN IT!- They have to witness you signing it.
A. It wasn't until I made it to Winnipeg and walked up to Canadian CBP(customs & border patrol) that I was told "you should have brought 2 copies of this"; only to be told 5 min later by another CBP officer that 1 copy is fine and they'll photo copy it.
B. While waiting at oversized baggage claim I was talking to some hunters from Kentucky and they go goose hunting every year in Canada and went through the 8hr course to get their P.A.L. (possession & acquisition license) which is the permit in Canada that allows you to own guns and buy ammo. I found it odd that a country with such strict gun laws as Canada would allow non-citizens the ability to hold a P.A.L. card but it worked for these guys and they didn't have to deal with the hassle, and come to find out they found an instructor for the class in Canada that wanted to come to the U.S. for vacation, so they paid for his round trip flight to the U.S. in exchange for his services in presenting the proper paperwork and 8hrs of instruction.(I thought this was a really good idea)
C. Your ammo must be in a separate checked bag and either in its original packaging or in a container specifically designed to hold ammo. This really isn't a big deal as my ammo was in the 20rnd reloading boxes and I never had an issue.
D. Get your self a GOOD case - airline baggage handlers are brutal
When it comes to Canada their customs and border patrol is no joke; and for all the regulations and paperwork and NOBODY seems to be on the same page! I believe this is because the laws for both U.S. but especially Canada are so complex that even the people enforcing the laws really don't know the true regulations.
Which brings me to the American side of things and to be honest with you while the Canadian CBP were a bit up tight about their laws, I was actually quite disappointed with how little training U.S. airline employees/TSA have when it comes to these matters and while we like to think of the U.S. as the land of the free, you better have your act together.
1. Read the airlines policy on traveling with guns as they differ from airline to airline, send a question email off to them if you are unclear on something and then print off their policies from their website along with copies of the answers they gave you to any questions.
2. We did not have any problems coming back into the U.S. with our guns, mainly because we came through the land border crossing in International falls Minnesota- However a good friend of ours recently flew back from Alberta on a goose/duck hunt with several friends and U.S. CBP tried to make them pay $300+ each in import duty because they couldn't prove they had their shotguns before departing the country - Even though they had their paperwork showing where they registered them in Canada upon arrival.
The solution to this is CBP form 4457 https://www.cbp.gov/sites/default/files/assets/documents/2017-Jun/CBP%20Form%204457_0.pdf
You take this form filled out and NOT SIGNED to the CBP at the airport before checking your bags and they will signoff on this voluntary form that you can present to CBP upon re-entering the U.S. as proof that you don't owe any import taxes on your previously owned guns or other expensive items - NOTE: Really good idea to have anything expensive listed on this form such as..... High end optics, sat phones, GPS units.
This form can be used for multiple trips- The guys from Kentucky that had their P.A.L. cards, also had these forms