Any office, department or agency provided for in this Charter with a name or with powers and duties the same or substantially the same as those of an office, department or agency heretofore existing shall be deemed to be a continuation of such office, department or agency and shall exercise its powers and duties in continuation of their exercise by the office, department or agency by which the same were heretofore exercised and shall have power to continue any business proceeding or other matter within the scope of its regular powers and duties commenced by any office, department or agency by which such powers and duties were heretofore exercised. Any provision in any law, rule, regulation, contract, grant or other document relating to such a formerly existing office, department or agency, shall, so far as not inconsistent with the provisions of this Charter, apply to such office, department or agency provided for by this Charter.