N.Y. Comp. Codes R. & Regs. tit. 9, § 6217.7
(h) The moving of voters from one county to another may occur as a result of a new voter registration form being processed or by any mechanism provided for in Election Law section 5-208.
(i) Applicable to transfers.
Any Board of Elections which receives information that a voter has moved to an address in another county in New York State which would have permitted such "from county" board to transfer the voter registration address within the county if the address indicated was an in-county change of address, shall send a copy of the address transfer information, including a voter registration number to the "to county" Board of Elections where the voter has moved. The "to county" shall, using such voter’s information contained in NYSVoter, including enrollment and signature exemplar, along with the new address information, place the voter at the new address pursuant to Election Law section 5-208 and provide notice to the voter in the manner provided in this section. When the "from county" forwards transfer information to another county Board of Elections for further processing, the "from county" shall send a confirmation notice in a form approved by the State board to the prior address of such voter in the "from county." Further list maintenance steps as required by this Part shall be undertaken upon notification by NYSVoter that the voter is registered at an address in another county in New York or upon notification received from the voter.