Invoking Common Law isn't an easy process, living together for a set amount of time isn't typically enough - you generally have to prove that you were living as a married couple, share bank accounts, both names are the mortgage/rent, filing taxes together, etc. I'd suggest that he discuss what his rights and obligations are with a legal professional. Chances are if the mortgage on the house is under his name, and if pays the associated taxes then he is the lawful owner.
Highly unlikely she has a case and is just using it as a 'threat' without understanding the implications. Again though, I'd run it by a legal professional.
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“If there is no struggle, there is no progress. Those who profess to favor freedom, and yet depreciate agitation, are men who want crops without plowing up the ground. They want rain without thunder and lightning. They want the ocean without the awful roar of its many waters. This struggle may be a moral one; or it may be a physical one; or it may be both moral and physical; but it must be a struggle. Power concedes nothing without a demand. It never did and it never will.” -Frederick Douglass
