No action or proceeding, civil or criminal, pending at the time when this Charter shall take effect, brought by or against the city or any office, department, board, commission, or agency or officer thereof, shall be affected or abated by the adoption of this Charter or by anything therein contained; but all such actions or proceedings may be continued notwithstanding that functions, powers and duties of any office, department, board, commission or agency or officer party thereto may by or under this Charter be assigned or transferred to another office, department, board, commission, or agency or officer, but in that event the same may be prosecuted or defended by the head of the office, department, board, commission, or agency to which such functions, powers and duties have been assigned or transferred by or under this Charter.