From and after the date of annexation any territory annexed to a special district is liable for payment of its proportionate share of any indebtedness then existing and payable by the special district. From and after the date of annexation the board shall levy upon all of the property in the territory annexed such taxes, tolls, or charges as are necessary to comply with the terms and conditions of annexation, in addition to any other district taxes authorized elsewhere in this division to be levied and collected.