Of course, if she does not cooperate in getting the money returned to her employer, in most, if not all States (certainly the 35 or so right-to-work states), she’d probably be fired as soon as the issue turned up in a reconciliation and it was determined that she did not let her employer know that she received the extra money.
The company will receive a reconcililation file, maybe paper probably electronic every month for the payroll account, which will list every check that cleared. It will contain at least a check date and check number and amount, which they can link to her payroll records. That will be all the evidence they need that she received the money.
If they’re on the ball, this will happen by the middle of November.
If the company is actually out the money they definitely need to be informed. Probably they aren’t. Bank errors usually only go one way, it’s how they’re caught, the Ts get all screwed up.