If the whole district is so included within one city, the district shall continue in existence for all purposes until a copy of a resolution adopted by the city requesting dissolution of the district or requesting transfer of jurisdiction over the district and the funds of the district to the city is filed with the board of supervisors whereupon the district shall be dissolved or jurisdiction over the district shall be transferred by resolution of the board of supervisors to the city, as requested by the resolution adopted by the city, and such funds shall be paid to the treasurer of that city and administered by the legislative body of the city for the benefit of the district.