The officers of an affected county shall immediately execute and deliver to the board of supervisors of the other affected county copies of all assessments or other proceedings relative to the assessment and collection of the current state and local taxes in the affected territory. The copies shall be filed with the respective officers of the affected counties who would have their custody if the proceedings had been originally had in that county and shall be deemed originals. All proceedings recited in the copies shall be deemed original proceedings in the other affected county and shall have the same effect as if the proceedings had been had at the proper time and in the proper manner by the respective officials of that county.