My son girlfriend is moving their daughter to another state.What rights do he have to stop that move?

Does he have court ordered custody and/or visitation rights? If the move would interfere with him exercising the court orders, then she has to get court permission for the move. If he doesn't agree, it could prevent the move.

If there are no court orders on custody especially on visitation, then she is basically free to move. He can try to stop her by filing for custody and visitation immediately. If the move is imminent he needs to be at the court tomorrow filing for an ex parte emergency hearing to temporarily block the move. He should do this not matter the current court status. The difference is the wording of the motion depending on current status. He should contact an attorney first thing tomorrow to start the ball rolling.

Agree with Scott, as long as he did everything he was suppose to do before, have custody order, have a child visit order, ( and he has been visiting the child) and he has been paying his child support,

He needs to ask the court to order her not to move, and if she would move anyway, order her to return the kids to the state.