If a person who is a party to a proceeding under this Act (not being a proceeding in a court) dies pending the proceeding, the Authority or the Registrar, as the case may be, may, on request, and on proof to the satisfaction of such Authority or Registrar, of the transmission of the interest of the deceased person, substitute in the proceedings his successor in interest in his place, or, if the Authority or the Registrar is of opinion that the interest of the deceased person is sufficiently represented by the surviving party, permit the proceedings to continue without the substitution of his successor in interest.