Ways to be added to Dad's account

I suggested to my sister she should be added to Dad's bank accounts (he's 88 with some health issues). Accounts and family are all in NY. Banker suggested there are 3 ways to do this.

They chose the "easiest" of the ways, which was using POA. I warned Dad that this way of doing it might undo her access to the account when he passes, because POA ends when he dies (I believe). The whole reason for adding her is so the account is accessible to her on his death. Am I correct, or are there nuances that I don't understand, like a durable POA?

Main question is "will she have access to his checking/savings when Dad passes"?