My boyfriend n his x girlfriend have shared joint custody of their 10 yr old daughter w physical to the mother can she just move out of state w her??

No, she cannot. If she has, your boyfriend should proceed to family court and file a petition for custody and a writ of habeas to return the child to New York immediately. He needs to do this quickly as NY will lose the power to hear the case once the child has been gone from the state for 6 months or more. Good luck.