(a) If the sentence of the court-martial extends to dismissal or a dishonorable or bad-conduct discharge and if the right of the accused to appellate review is not waived, and an appeal is not withdrawn under Article 61 of this Code, that part of the sentence extending to dismissal or a dishonorable or bad-conduct discharge may not be executed until there is a final judgment as to the legality of the proceedings. A judgment as to the legality of the proceedings is final in such cases when review is completed by the Illinois Appellate Court for the Fourth District as prescribed in Article 67a of this Code, and is deemed final by the law of this State.
     (b) If the sentence of the court-martial extends to dismissal or a dishonorable or bad conduct discharge and if the right of the accused to appellate review is waived, or an appeal is withdrawn under Article 61 of this Code, that part of the sentence extending to dismissal or a dishonorable or bad-conduct discharge may not be executed until review of the case by the senior force judge advocate and any action on that review under Article 64 of this Code is completed. Any other part of a court-martial sentence may be ordered executed by the convening authority or other person acting on the case under Article 60 of this Code when so approved under that Article.