This explains it all: https://www.nraila.org/articles/20150101/guide-to-the-interstate-transportation
That said, I m a NYS CC Permit holder. It is my duty to know the laws of each state. You cannot legally posses in NYC without written consent by NYPD. I have family on Long Island. I could carry to LI from my county with my weapon stored the way it is explained in the first two paragraphs of the article without consent but can be arrested for it. If I dont get consent first I do not carry "through" NYC. That said, I also have a Utah permit that gives me lefal right to carry 42 states the time. That has changed in the last 9 years since I got it. For instance Pennsylvania no longer accepts the Utah Permit. But I can in Delaware. So, I can travel under US law through Pennsylvania without overniting to go to Delaware with the proper transportation requirements in the first two paragraphs. NYS does not recognise any other states carry permits so the Alabama permit does not hold give him permission in NYS and if he did not get permission in NYC he is screwed.