death of a customer

Recently one of our customers had passed away. Her daughter had contacted us to let us know. According to her daughter, she had no will and hence there is no executor for her estate. The daughter has been keeping the rent up to date by sending us payments and has advised us that she would like to continue renting the unit until she’s able to clear it out. Also, before the customer had passed away, she had called us while she was in the hospital to verbally request that her daughter be added to her list of authorized access persons to her storage unit in the event that something happens to her. I’m personally familiar with the customer and recognized her voice so I knew it was her that was calling us. My question is – should we allow the daughter to have access to her late mother’s storage unit? At this point we’ve asked her to provide us with the death certificate as proof that her mother has, in fact, passed away. My concern is that someone else comes out of the woodwork claiming that they are entitled to something that was stored in the unit and they have a legal document (such as a will) to support their claim. Please note that our rental agreement doesn’t state anything regarding what to do in this matter and as such, any advice on this would be appreciated. Thanks.