Legal Question in Family Law in Texas

No, there is no such form. Due process would require that any change of custody (or any other change to the paternity order) requires that the father be notified and be allowed to tell the Court his side of the story.

First, unless you have had a court action, paternity has not been legally established.

Second, you must have a court decide your rights as the father is as entitled to rights to the child as you are. However, if you move to California then California will be the home state of the child after six months and any court case must be brought there. Of course, if you move, the father might file a case in Texas within the next six months. It would be wise to compare the Texas and California laws as to possession and child support before making a decision.