Be it further enacted, That no action or proceeding, civil or criminal, pending at the time when this Act shall take effect, brought by or against the city of any office, department, or agency thereof, shall be affected or abated by the adoption of this Act. All such actions or proceedings may be continued notwithstanding that the functions, powers, and duties of any office, department, or agency a part thereto, by or under this Act, may be assigned or transferred to another office, department, or agency, but in that event the same may be prosecuted or defended by the head of the office, department, or agency to which such functions, powers, and duties have been assigned or transferred by or under this Act.