It depends

By the law, her H1 will be automatically extended after 6 years only if she is still working for the same employer. That is why INS asked her lastest pay-stub. Likely her GC case will be denied.

I have a friend, who applied her F1 after her H1 had expired for 2+ months. She got her F1 now.

It seems that your friend does not have any choice except applying F1. Why does not she try? Oh, marring a person who has a legal status may solve her status problem.

Good luck.