If he currently has permanent custody, has lived in the new state long enough to establish legal residency and the are currently no issues in front of the court, he can request jurisdiction be move to the state the children are legal residents of for future court actions. Yes, he will have to go through the original court for approval and the new state will have to accept it. Nothing is automatic. Nothing concerning the original order changes. It only means that any FUTURE action will be filed in the new state.
The original state has the RIGHT to continuing jurisdiction, but most courts have no problem transfering it and lightening up their own case loads a bit.