Dear Teresa,
I'm sorry for your loss. The power of attorney doesn't help your mom in this situation because the power ceased at your dad's death. Because the loan was only in your dad's name, his passing triggers the reverse mortgage to come due. Review the loan documents with your mom. You shouldn't assume she has 12 months before the lender requires action.
At this point, the will, or state law if he died without a will, determines who inherits the home. I'll presume it's your mother. She has the option to refinance the home, sell it or turn it over to the lender. If it's just turned over to the lender, she may lose any remaining equity she has in the property.
If there is still equity in the home and she sells it, she can pay off the reverse mortgage and keep the net proceeds. If she decides to refinance, she can look into refinancing with another reverse mortgage. It'll mean another round of closing costs, which will be expensive, but she won't have to worry about making a monthly mortgage payment. Alternately, she can look into refinancing with a conventional mortgage. Her ability to qualify for that mortgage, depending on her income and credit history, will determine the viability of that option.
The minimum age for reverse mortgage borrowers is 62 not 65, so it's not clear why the reverse mortgage wasn't in both of your parents' names if your mom was 62 when your dad took out the mortgage. What's done is done. What's more important here is that your mom doesn't have to wait until she's 65 to apply for a new reverse mortgage.