It seems like you could be charged with providing a false statement / or identity theft. You should contact a criminal defense lawyer in the area whir the conviction occurred.
The person with the new charge should be able to show that there record is incorrect, by providing proof of employment during the time of incarceration.
This is a complicated case, and the answer depends on whose interests you are putting first, i.e. yours or the person whose name you used. The other person (let's call him Joe), if convicted, will be sentenced as a second offender. When he learns of the first offense, he can make an application to the State of Florida to re-open the case and have the conviction set aside based upon identity theft. (Believe it or not, this is not the first time something like this has happened.) As long as Joe can satisfy the Florida Court that he was not the actual person who was issued the summons and appeared in court, he does not have to necessarily know who it was that used his name (although it would be easier if you came forward and acknowledged that it was you). If the Florida Court sets aside the conviction in Joe's name, Joe would then be facing only a first offense in the State of New Jersey. If Joe does not know it was you who used his name, and you do not come forward, it is unlikely that you will get caught. Please bear in mind, however, that if Joe does know that it was you and decides to point the finger in your direction, you could be charged with providing false information to the police or even perjury for making false statements under oath in court. You should definitely contact a lawyer for more specific direction on how to address this problem.
You have been given some great advise so far. Make sure that you get counsel in your home state to assist you with your decision. You didn't say whether or not you care what happens to the person you hung a criminal record on in the past. That makes a difference. The person accused should hire great counsel and demand proof (fingerprint, booking photo, booking information, NCIC check) of the past conviction. The "proof" should exclude that person from being charged a second DUI. Evan Levow is an Avvo.com rated attorney in Jersey and he can definitely give you some great advise.
First, go speak to a Florida licensed attorney about these charges and you potential exposure. You have no duty to incriminate yourself, so I would invoke your right to remain silent. As for New Jersey, you could be prosecuted for identity theft, obstruction of justice, false incrimination,and possibly other violations. Again, invoke your right to remain silent. The other person ought to be able to establish that it was not him, but in doing so it may be revealed that it was in fact you, especially if there are any pictures, or if he knows you. So, you should also contact a NJ licensed attorney.