No former judge of the New York State Court of Appeals or former justice of the Appellate Divisions or Appellate Terms of the Supreme Court of the State of New York shall appear in person in the Appellate Court on which he or she served, or use or permit the use of his or her name on a brief filed in such court, within two years after having left such court. Nothing in this Part shall prohibit a law firm with which said judge is associated from appearing before a court and using the name of the firm on its papers consistent with that appearance.