Thanks to all who answered - I now have a better idea of the possibilities, and can at least make a start in attempting a resolution.
I seem to have ruffled some feathers among those who responded, but (as I said) there is a lot more to the situation which I don't want to air here except to say that the subjectivity of the concept of fairness goes only so far. You could say (and some do) that segregated bathrooms in public facilities weren't really unfair because the concept of fairness/unfairness is subjective, and some people's subjective opinion is that they were perfectly fair. But I think most reasonable people are willing to draw a line and take a stand at some point, and I don't have a problem with saying so when I believe something is unfair. Obviously I don't expect the law to reconfigure itself on the basis of my objections, but I think I can state them anyway.
I think that I will put it bluntly. The concept of fairness from anyone's personal point of view is completely irrelevant here.
She is a co-owner of the house. No one, not even a judge, can take that away from her. It doesn't matter that the mortgage is in his name only, it doesn't matter than he has made all of the mortgage payments.
The only thing that he can do is file a partition suit, which is very expensive and usually results in the home being sold at auction and the proceeds (if any) used first to pay the attorneys and second to be split between the owners.
The results of a partition suit are rarely advantageous to the owners.
Therefore, the only thing he can do is try to come to a resolution with her. If the house has any equity, he might offer to buy her out for her 1/2 of the equity.