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Are you asking if you are liable?
The reality is that there is really no way of raising cast iron proof. All you can really do is raise the evidence that you have.
The problem here is that even if you didn't sign the agreement, the money went into your account and you didn't report it. That tends to suggest you must have known.
If you are intent then you can refuse to pay and invite them to sue and then defend on this basis at court but this is fairly strong case.
The police should investigate though. At least a prosecution of her for forgery would be helpful.
Can I clarirfy anything for you?
The police could do a handwriting analysis but that is a bit his and miss. Yes, they could prosecute. Whether they will or not is another matter.
Even if they do not though, an allegation alone would be helpful.