Agreed, if girldfriend is not in the US right now, this is fraud. In this case @Danny84 it doesn't matter whether she knows or not, of your plans of filing for AOS. The immigration fraud committed by you or her is still fraud. Then yes, it's illegal and very risky. It's not uncommon for IO to carry out stokes interview for suspicious couples, e.g. separate both of you and question during AOS interview. If IO smells fraud, you're in big trouble as well as your girlfriend.
If she's back in Mexico, go marry her there. Have a beautiful wedding inviting all of your and her relatives, file CR-1 and have straightforward immigration.
Good luck!