Yes, a New York State resident can legally purchase a compliant long gun (rifle or shotgun) from a Federal Firearms License (FFL) dealer in another state, including a neighboring one, and take possession of it there, provided the transaction complies with the laws of both states. you can buy...
New York State implemented its own enhanced background check system, linked to the federal NICS but with state-specific requirements, under the NY SAFE Act in 2013,
NEW YORK'S GUN LAWS this is clarified in what was sent to dealers if they bothered to read it
GUN DEALER REGULATIONS
Sale of Guns & Ammunition
“Seller of ammunition” is any person, firm or corporate entity engaging in the business of purchasing, selling, or keeping ammunition, but this...