Since they are legally married, she has to pay him a minimum of the BAH2 rate every month or she can face disciplinary action. He doesn't have to report the marriage as fake, but she is required to support him because there is a legal document. Same goes for medical benefits and everything else. All he has to do is say its not fake. She is just threatening him.
Have him contact her first. If she refuses, then go to her chain of command. If the chain of command doesn't help, go to the post Inspector General.
Again he doesn't have to say anything about the marriage being fake. If she decided to go for divorce, she would have to pay for his lawyer and he could possibly sure for a portion of her retirement benefits as well under the Military Spouse Protection Act.
As far as her not signing a divorce paper, that doesn't matter. A judge can order it. Only one party has to want the divorce.
As for both of them getting into trouble, I think it will be mostly her that gets into trouble. Its government has its claws in her already and UCMJ doesn't apply to him. The federal government would have to decided to pursue him. Only the military has to get her.
Overall, she is in the worse position.
Overall, I suggest he does not say anything about it being fake, that he demands his entitlements and becomes a troublesome husband, she will either have to pay or file the divorce.
He has the power here because she is obligated to support him. He can claim his legal entitlements and leave it to her to admit it was a fake relationship. And if it does go to that, if he has evidence she is a lesbian, that even more trouble she gets in.