Legal Question in Employment Law in California

It would be proper to do so. Your new employer should then be confident about your integrity.

if you are correct, at some point your employer will discover the over payments and may ask you why you did not report it. When you have no reason, they may fire you.

No, you could just wait to be fired, sued and criminal charges brought against you for theft, if they are making an overpayment mistake and you take advantage of it by using the money.