The aop is invalid because the actual mother did not sign the aop, well, the person signing it claimed to be somebody other than the actual mother.
Once maternity is established the aop is worthless since the person it claims to be the mother is now proven to not be the mother. While an argument can be made the actual mother did in fact sign the aop using a false name, until that is adjudicated the person named as the mother will in fact be proven to not be the mother rendering the aop invalid. There will be no proof of paternity since the person named as the mother could not legally acknowledge the father as being the father.
Sure once the true mother is proven to be the mother and correctly identified as such they can stipulate paternity but given the major screw up I would suggest it be simpler for dad to file a paternity action where he is adjudicated to be the father based on a dna sample. As it stands all the named mother has to do is dispute the authentication on the aop and its claim will be in legal jeopardy leaving the named mother as the only person a court is going to acknowledge as a parent until other court actions are filed. It would be very easy for the named mother to prove it is not her signature on the aop.

