Laws on "found property" probably vary from state to state.
In Florida found property is supposed to be turned in to the local police department, who will then hold it for 90 days. After the end of the 90 days, if no owner has come forward and proper notice has been given (through newspapers is accepted) then it can be claimed by the person that found it, kept by the police department, or sold at auction by the dept.
In your scenario there is no proof of the original owner of the money, it is only assumed to have belonged to the old lady.
Actually had a guy in a hotel next to the Miami airport call to say he found a "bag of money" in the ceiling. I was assigned the call and ended up counting 3 million Italian Lira. (At the exchange rate at the time approx $150,000 US). I impounded the money and 91 days later the guy was at the police station with his attorney and a big smile. My dept had to give him the money.
This isn't Burger King, you are not going to get it your way.