Unfortunately, there isn't enough information in your question to try to answer. It isn't clear what paperwork the State might file that would have anything to do with your son appealing a criminal case.
In Florida, your son's attorney has certain professional obligatons to file specific paperwork if your son wants to appeal, not the State.
Because you say you're looking for appellate counsel already, the best suggestion I have is to do that: there are a number of qualified criminal appellate attorneys all over the state who will be happy to give you a free initial consultation, and get the details from you that may help them answer your question.
Wishing you and your family the best,
Keith
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