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I'm sorry to hear about your situation. In the absence of a parenting agreement and/or custody/visitation
order that would say that she's not allowed to do this, she can. Such a clause is called a "morality clause". There needs to be some sort of binding language (contract/court order) that limits her rights that she otherwise has (such as moving in with a boyfriend). There are no laws that say that this is illegal, and so the restriction would need to be done by a court or by agreement.
If there's no court order or agreement in place, she could do this, but your son could still seek a modification of custody in light of her actions if he could establish that this is not in the "best interests of the child". Ultimately that would be up to a judge to determine, in light of all the facts of the matter.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!