Except as provided in subdivision (b) or (c) of Section 15600 and Part 9.5 (commencing with Section 15670), the department is the successor to, and is vested with, all of the duties, powers, and responsibilities of the board. All laws prescribing the duties, powers, and responsibilities of the board to which the department succeeds, together with all lawful rules and regulations established under those laws, are expressly continued in force, including, but not limited to, existing processes and remedies available to a taxpayer or feepayer such as settlement options and appeals processes.