I would agree with the previous poster. If your license is suspended in NJ it is unlikely that NY will issue you a b license. As a matter of fact there is a law that specifically deals with that, if you are suspended in one state you cannot get a commercial license in any other state. If you had a DUI in NJ and you got reinstated then NY would issue you a license. Check with the NJ Motor Vehicle Commission (the same agency as the NY DMV). It is a huge pain to get anyone who is human on the phone but they will be able to help you.
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If your privileges are suspended in NJ (NJ can't take your license only your right to drive in NJ) Trenton will advise Albany and NY will suspend your license there. NY is a member of the compact and they do suspend on NJ convictions. How that affects you NY situation should be asked of an NY lawyer. I do not even know what an A B license may be.
Gee, I am the only one here who disagrees. NJ and NY are members of the interstate compact, which only means the NJ will report it NY and that NY may take action. It does not mean they will honor the full suspension. Each State has their own procedure for handling out of state convictions. In fact many states will NOT suspend you for a first offense, out of state suspension. NY offers first time offenders a work license to get to and from work, school, and other very limited use necessities. What you need to do is contact a NY lawyer or NY DMV!