I don't know whether to believe her either, but these things can be done by criminals perpetrating identity theft. The following assumes she can be believed.
If the police really did say they can't prove anything because he forged her signature then they seem to be saying they accept it was forged. If they do accept that, it is a criminal offence and they should be pressured to prosecute. If they are unsure, it seems likely a handwriting expert might be able to confirm whether the signatures are forgeries. If this is accepted then, whether or not the police prosecute, the lenders should cease chasing her for the debt.
Also a note should be put on all her Credit Ref. Agency files to warn potential lenders in case he tries to do the same again.