personally, I think she should
I think she should have left the country under that false name and then re-enter with her own information. And she should have done this BEFORE she married her hu*****and.
Since her hu*****and is a citizen, she will have no trouble getting here LEGALLY. But now, it is all lost. I doubt that she can withdraw her application at this late stage without drawing suspicion.
So she can only hope that no one will ever find out. Because if they do and no matter when, her GC can be revoked because she got it under false pretense. I don't think she will be charged criminally, because it is easier for them to deport her.
I do hope that she won't bring her son into this. Because, I can't imagine the kind of dark cloud that her son will have to live under too just because his mom made a judgement error.