N.Y. Surr. Ct. Proc. Act § 714
Whenever the supreme court shall suspend or remove or accept the resignation of a guardian of an infant's person or property or both, or of a testamentary trustee appointed by it, a certified copy of the order or decree shall be filed in the surrogate's court of the county having jurisdiction of the infant's person or estate or of the testamentary trust and a minute thereof shall be made and indexed in the book or books kept by the surrogate in which similar orders or decrees made in each surrogate's court are entered.
The county clerk of the county in whose office the order or decree of the supreme court is entered, shall give written notice to the clerk of the proper surrogate's court of the filing of such order or decree.
N.Y. Surr. Ct. Proc. Act Law § 714