Hello. Because her name is XXXXX XXXXX the house she technically does "own" half of it whether she is paying the mortgage or not and the police would not prosecute her under these circumstances. They need to come to some kind of agreement on the personal belongings in the house (who owns what), because she will simply continue to help herself to whatever she wants when he is out. If they have an agreement and then she enters to take items, she can be prosecuted for it and sued civilly for the value of anything else that she might take that was not specifically agreed to. If she refuses to come to any specific agreement, he is then in a position of having to try to file a civil complaint with the court for return of the items (in order to force the issue) and at the same time, he should seek an order to divide personal property so that she does not have any excuse to enter the house without knowledge or permission in the future.
Regarding the mortgage, the court can order it sold -- and they will equally take a hit on their credit reports, and the divorce court can order that they split the debt 50/50 -- but the mortgage company does not care about that and does not have to follow the orders of the divorce court and will sue either or both of them. And unless there are minor children involved, the odds of having the court order her to help make mortgage payments for a house that she is not living in are small (even when there are minor children involved, the court typically orders the house sold, but may give a bit of time before that happens). Because of the ineffectiveness of divorce agreements and state laws regarding divorce this is why many divorcing couples simply walk away from a property that is underwater -- because neither party wants to continue paying the full mortgage payments and there is no real way to make the other party pay the payments.
So, his only real legal recourse here is a civil complaint -- he can try the divorce court, but because the divorce is "final" it would be quicker and less expensive for him to file a small claims suit against her to force her hand so they can at least come to an agreement regarding what she can remove from the house and what items are to remain his property. I wish that I had better news for you, but until he sells the house or walks away from it, there isn't much he can do about her taking personal items unless there is an agreement in place regarding the items in the first place.
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