If the district board approves the proposed annexation, or approves the annexation but excludes any lands, a certified copy of the resolution of the district board, together with a map or plat of the new boundaries of the improvement district, shall be filed with the agencies designated in and as required by Sections 54900, 54901, and 54902 of the Government Code. Upon such filing, the annexation of the territory to the improvement district shall be effective.