Mom Leaving state with children

I just posted a few days ago. Learned the mother is moving out of the jurisdiction with kids. If she leaves this state how soon can the case be transfered?? Can the dad file asap in his state if the children are not legal residents of the new state yet?? The mother also let him know tonight that until he catches up on all the money he owes she will not let him have anything to do with the children. She also is coming into town but he wasn’t supposed to know because she isn’t going to let him see them.