I'm sorry to hear about your sister. Unfortunately the savings account will pass according to the beneficiary designation most recently filed with the bank. The beneficiary designation cannot be changed now that your sister has passed.
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The promise is probably unenforceable especially if you did not take any action in reliance of it.
The signature card will be determinative.
I think you are out of luck. Sorry,. Certainly, you can check in with a lawyer and one who practices in whatever jurisdiction where your sister lived when she died is the right place.
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It depends on how much is in the estate and what procedure to use but if there is no will then you can't be named a primary beneficiary post death without an agreement of all potential beneficiaries. Probate her estate or seek the services of a Probate attorney to help.