(a) All contractual claims against the City shall be filed with the Clerk, who shall transmit them to the Council.
(b) The Clerk shall verify the correctness of each claim and, subject to further procedures established by the Council for auditing and approving claims, he shall approve for payment each claim so verified, if a sufficient appropriation is available for the purpose, and, upon the approval of the payment thereof by the Council, shall draw and sign a check therefor. Each such check shall be countersigned by the Treasurer, who shall make a proper entry thereof in his books of accounts. Any officer who signs or countersigns a check on any funds of the City, except as herein provided, shall be deemed guilty of a violation of this Charter.