Estate Law Questions? Ask an Estate Lawyer.
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1. Did she own 100% of the shares of that corporation?
The bank will assist you in opening an account in the name of the estate so you can pay bills and accept deposits. The bank will require proof that the probate court legally confirmed your appointment as executor. So you will need to take with you what are called "letters testamentary" (sometimes called "surrogate certificates"). These are certified documents issued by the probate court that prove you have the legal authority to act on behalf of the estate.
As far as having authority to act on behalf of the corporation, you would need to access the shares transfer ledger that came with the minutes book and transfer the shares from her name to the name of the estate and then adopt a corporate resolution electing yourself to the board as the executor and then naming yourself as president of the corporation. Since she owned 100% of the shares; this is all internal and should not be a problem.