The board succeeds to and is vested with all of the powers, duties, purposes, responsibilities, and jurisdiction vested in the Department and Director of Public Works, the Division of Water Resources of the Department of Public Works, the State Engineer, the State Water Quality Control Board, or any officer or employee thereof, under Division 2 (commencing with Section 1000), except Part 4 (commencing with Section 4000) and Part 6 (commencing with Section 5900) thereof; and Division 7 (commencing with Section 13000) of this code, or any other law under which permits or licenses to appropriate water are issued, denied, or revoked or under which the functions of water pollution and quality control are exercised.