After making all necessary and proper changes in the boundaries, the governing body may, by a resolution passed by a two-thirds vote of all its members order the annexation to the district of all or such part of the territory originally proposed to be annexed as the governing body determines will be benefited by such annexation and shall describe the boundaries of the territory annexed. This resolution, together with the names of the members of the governing body voting for and against the resolution, shall be spread upon the minutes of the governing body. Certified copies of the resolution shall be recorded and filed in the manner and with the same force and effect as provided in Section 4613.