The county clerk, upon being furnished with an order discharging a mortgage of record, as provided in section 1931 or section 1932, and, in the city of New York, the register, upon being furnished with a certified copy of such order, and upon payment of the fees allowed by law for discharging mortgages, shall record the order and discharge the mortgage of record.
N.Y. Real Prop. Acts. Law § 1933