Legal Question in Civil Litigation in Louisiana

Whether your stepson must register in Texas is a question of Texas criminal law, not of Louisiana civil litigation. I recommend re-posting it under the correct state and subject.

Your question does not say when your stepson was convicted, what sentence he received, or whether he has served that sentence. If he hasn't served his sentence yet and if he was supposed to start by now, then he is a fugitive from justice and should get a Louisiana lawyer right away to help prevent matters from getting worse. That seems like a much more urgent concern than whether he must register in Texas. After all, if the Texas authorities learn that he is a fugitive from another state, they will arrest him immediately and invite Louisiana to seek his extradition.