No. This is not a legal arrangement. She may nominate you to serve as Personal Representative and decline to do so, herself. But she cannot appoint you. This must be done by the court. The court is the only entity that can give you legal letters of authority.
A probate may need to be administered first. You will need a valid power of attorney to obtain the assets once the estate is complete. I suggest that you meet with an attorney to address nest steps. It not as easy as just picking up someone elses stuff.
Without reviewing the specific document you refer to, it is not possible to render any opinion or to provide an answer. You should take the document and all paper relating to your friend and her husband to an attorney who specializes in estate administration. This way you can get your questions answered and determine the proper steps to take.
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