The US GC residency requirements are not as clear cut as the Canadian rules. The US says you can not be outside the US for more than a year at a time without getting permission. Preferably less than 6 months to avoid any questions. They can also revoke the GC if they believe the person has moved to another country permanently. However, it is unclear how much you must have lived there. I have known people in the past who have kept a GC alive for years simply by visiting the US every 6 months.
So.. if you marry the lady and sponsor her for Canadian PR, you'd have another problem and that's her having PR of two countries. Now, there aren't any rules that forbid that. She could live in Canada and still try to keep her GC alive by visiting the US at least every 6 months. She should use the US GC to enter the US and the Canadian PR card to enter Canada. However, as both countries work together, she may run into immigration officers who will tell her that she can't have both but there is actually no law in either country that says that you can't. If she is faced with something like that, she should just say that she didn't know that and that she will look into it and then brush it off.