As educators, it's our responsibility to know our material, and be mindful of what we tell others. Thankfully, a few sections of the laws are clear-cut and direct. Try this link, spend a little time familiarizing yourself with what the laws are, not what you hear via third-party. Some folks can mislead us unintentionally and unknowingly.
New York Penal Law - ARTICLE 400
LICENSING AND OTHER PROVISIONS RELATING TO FIREARMS
§ 400.00 Licenses to carry, possess, repair and dispose of firearms.
6. License: validity.
Any license issued pursuant to this section
shall be valid notwithstanding the provisions of any local law or
ordinance. No license shall be transferable to any other person or
premises. A license to carry or possess a pistol or revolver, not
otherwise limited as to place or time of possession, shall be effective
throughout the state, except that the same shall not be valid within the
city of New York
unless a special permit granting validity is issued by
the police commissioner of that city.