Sorry, I am not sure that they will consider a permit from a different state. I'm guessing that they will not. You will most likely be expected to start over. You can run it by the clerk at the counter. If they can retrieve your info from the system online and issue you a NJ permit based on the info there that would be nice but I can't imagine anyone reaching out that way, especially if its not an option from DMV.
No would probably have to do the whole test over
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