The department may issue a certificate of convenience to the executor or administrator of the estate of a deceased broker, or if no executor or administrator has been appointed, and until a certified copy of an order making such appointment is filed with the department, to the widow or other heir otherwise entitled to conduct the business of the deceased, permitting such person to act as a broker in the conduct of the business of the estate for a period of 90 days from and after the date of death pending, but not later than, disposal of the business unless such person qualifies by examination for and obtains a permanent broker’s license. The department may extend the certificate of convenience beyond the 90 days on the showing of a just and reasonable cause.