Once she quits her job, she will be AOS only. And she can work under EAD (get her EAD ASAP, so she can find another job quickly if she wants). Once she uses her EAD, her H4 is no longer valid. So what's the point of applyfing for an H4? A waste of money.
AOS alone will allow her to stay legally until her GC arrives.
AOS alone will allow her to stay legally until her GC arrives.