My sister took my mother to the bank under false pretenses and added her name to her previously solo account. What can I do to prevent this?

You as POA have a right to legal advice.
As someone with a fraudulent and nefarious sister you need that advice now.
First of all, make certain this is an ironclad POA you have by a good attorney.
Make a phone call to that attorney now with your question; we are a Forum of strangers, not legal help, and our advice to you isn't reliable as such.

It is very important that whatever banks and other entities that now hold your mom's funds knows that there is a fraud alert, that you are the signee, because sister can, I am certain--as she has once done--sign now YOUR name to anything she wants.

I think her attempts should be reported as an attempt to defraud, but an attorney will let you know if/how to do this. The important thing now is to prevent recurrence.
Someone into theft on this level is a DANGEROUS threat to everything your mom has. Thank goodness you caught this and the bank was cooperative. And can only say if they were, you have a good POA indeed.

Yes because your sneaky sister will try and Pull another Move . Do Not let this person alone with your Mother - she is a criminal .

How did you learn of this incident?
And has your mother's bank since removed your sister as a signer/ co-owner of the account?
You say you filed a POA with the bank. Does that mean you now have power of attorney over your mother's financial affairs, and access to her bank accounts?

If you have control of the money, create a separate account and move the money to safeguard it from any bad actors.

And, of course, you can have an attorney send a letter to anyone, warning of legal action. But you should consult said attorney first to see if you have a case.

I don't know the legal answer to your question, but do you have online access to your mother's account? If so I suggest checking it daily so you catch anything like this right away if it happens again. I'm glad the bank restored the money. It can be shocking how adult children can take advantage of a parent's trust to improperly use their money.

How do you know what your sister told your mother at the bank? Does your mother have dementia? Is your sister her caregiver? If she is then it makes sense to have her name on the bank accounts.

Geaton is right. Your story doesn't add up. I am on my mother's bank account only because it makes sense for me. I am her POA. I was added when she was in her late 70's and there was no need to show any POA documents.
I had to show plenty of identification and so did my mother. Then we ordered checks.

Believe me, if your mother was baffled and confused and the bank employee they were sitting with (this is not done in the teller line or drive-thru window) heard your sister lying about her only proving her signature they would not have put her name on your mother's bank account.

Your sotry doesn't add up.

Speak to an attorney for an answer to your question. We're just a forum of caregivers.