Federal law requires banks to allow family members to assume the mortgage if it's left to someone at death, but the same does not apply to unmarried partners. If she can afford the mortgage and credit is okay, there is a good chance they will let her. If they don't let her, she would need to either secure a new mortgage with another lender, or sell the house and she can take the equity and buy or rent somewhere else.

One idea is to have a secret courthouse wedding right now and then save the full wedding event with family and friends for later. Nobody has to know but you two and the justice of the peace.