If a wife filed and was granted a divorce but the paperwork was never filed, can the husband have the paperwork filed?

I am not sure that I understand your question.  I will presume that the Petition for Divorce was filed.  I will also assume that a court appearance took place, the divorce judgment was rendered and the Judge ordered that a judgment be submitted.

Usually the Court will order one party's attorney or the other to submit the judgment.  The Court's minute entry will reflect who was to prepare and file the judgment.  Unfortunately, sometimes judgments never get submitted to the Court.  If no judgment has ever been submitted, then you would have the right to submit a judgment to the court.  You would have to send your spouse's attorney a courtesy copy of what you intend to file with the court.