If you have POA, like the others have said, make your address her legal address so all bills, tax documents, bank statements, brokerage statements, Medicare EOB and anything from Social Security, etc. come to your address. This will be the address that you will use for her for tax document and anything legal.
You could give her Assisted Living address to friends and family who might want to write to her.
Many assisted living places do not have a secured mail box for the residence so keep that in mind.
Sometimes residence may pick up the mail of others by mistake or because they have a mental impairment.
You probably need to change her address officially to your address on Medicare and Social Security. Sometimes this is a problem when picking a Medicare plan since they are by area but if you are not very far from her, this is no big deal.
If there is a need, now or later on, she needs to add your name to the Medicare and Social Security file so that you can talk to them about any matter. If she becomes mentally incapacitated, you will have to become a Representative Payee on Social Security - this only means that you are authorized to spend this money for her benefit and will have to account for such with them.
It's Always Something . . . . Roseanna Roseannadanna