The proposed will needs to be filed in the surrogate court in Fl. If it is rejected then an application must be made for an intestate administration. It is best to use a Fl probate attorney. NO ONE distributes an estate from a will, you need letters of administration from the FL court. Also if there are witnesses to your father's will or the name of an attorney drafter, they might know where the original will is.
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Mr. Sarno is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Sarno strongly advises the questioner to confer with an attorney in their own state to acquire more information.
You and your family members, if any, can gain access to the bank account through the Florida Probate process. If the account is valued under $75,000 you can utilize the "Summary Administrative" process. You will need the assistance of a Florida attorney, however, it is a relatively quick and low cost process. Feel free to contact me (email@example.com) if you would like me to assist you with the process.