Yes - you can pay the fee in advance and wait until you get back to Canada to file the sponsorship.
A few things though - entry into Canada is never guaranteed for non -canadians, and if you show up with your husband and a U-haul, it's not sure that they will let him in - I'm not saying that he will be denied for sure, but there is always a risk that the agent at the border doesn't appreciate the fact that you are moving.... technically,your husband can not "move" to Canada until he has his PR. He would be visiting. While it may seem only a lexical difference, it can actually happen at the border, so I would prepare with caution there.
Also - it's not because your husband is in Canada that you have to file inland - he could be in Canada with you and file outland. If you file inland, both sponsor and sponsored person need to stay in Canada for the duration of the application (inland is currently 14 months, and going to 16...). So - think about all the options and read here, wait for more answers maybe from US/Can couples, and make sure you have the full overview of the process before you start.
You can also start the process while outside of Canada ( as you are a Canadian citizen), and then go to Canada in the middle of the process, if you're filing outland.
Police Certificate expire 3 months after they are issued, so make sure you time everything right.
Don't take CIC agents's words over the phone too literally - telling you that "all you need at the border to cross is a police certificate, marriage certificate and the fees" is plain wrong : it helps to have that, but it won't necessarily get entrance for your husband - as I said, it's a little more complicated than that. US citizen are rarely turned down at the border, but it does happen, so I suggest you prepare for the move by reading more experiences here.
Good luck,
Sweden
