I'll ask the game and wildlife officers when I get to Alaska...they were just curios i would like, but if they're restricted its no big deal.
It would be the US fish and wildlife dept., and Alaska dept. of Fish and Game.
Brown bear skulls and claws may not be bought, sold, traded or bartered. They can be given as gifts, however both departments get a little weird about skulls without seals on them, brown and grizzly bear skulls are supposed to be sealed. It is possible sometimes to get a courtesy seal put on "pick-ups".
To drive through Canada with them would be a big mess, also to bring them to Australia, if you wanted to do that sometime would be a big mess. Many times it's better to just mail the stuff but you need to be sure everything is on the up and up because interstate shipping, either by mail or carrying it, of shady wildlife materials is in violation of the Lacey Act, a federal offence which carries stiffer penalties.
For instance, sometimes people shoot bears close to their homes for safety reasons, that is understandable. The lawful thing to do would be to report it, skin it and give the skin and skull to wildlife officials. I am not saying this is the case but if you think it is possible, the best thing to do is leave them where they are. Officials get suspicious when someone says "My friends found this on their property and gave it to me."
I'm not trying to mess in your business, hope I was helpful, have a good time in Alaska, if you go through Fairbanks be sure to stop at my store and say Hi, I'm always happy to meet people from the forum.