Oddly, the answer might depend on the person and personality at the bank or other institution"”and exactly how you held the power to deal with your mom's money.
The address on the check is not controlling here.
If you were listed as joint owner of the accounts or as the designated payor, then you have the easy and commonsense ability to cash the check and accept it as your own funds"”or those to use to finalize your mom's last expenses.
However, if you are operating alone as your mother's named power of attorney, after her death, you are no longer empowered to act for her; powers granted in a power of attorney end at the maker's death. It is likely you have the right to sign and deposit the check only if you are acting as your mother's executor or trustee"”that is, she named you to act for her after death in another document: a will or trust document.
If no such paperwork exists, then contact the bank holding the account in which you want to deposit the check"”and ask for advice on how to proceed. Many financial institutions have their own forms and formats to follow in these situations. And working with them in that way, you may also be able to avoid some pesky probate paperwork.