You should be able to get the death cetificate from the funeral home. That is the standard procedure. Someone will have to file to open probate and be named the personal representative. No one does this for you. If she has blood relatives, they will be first in line to be named PR but there is no reason you can't file.
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You would file because the Trust Co says someone has to in order for you to get your money. I don't have a crystal ball and had no idea of any other relatives. Check the obituitaries. The local paper is usually online and it will list the funeral home.
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Practicing attorney with extensive experience in wills, estates and trusts