Appeal Case in Florida State did not file for extension or file brief

Although, based on your question, you called the failure of opposing counsel to file its answer brief by the due date to the attention of the District Court of Appeal, it is my experience that the Clerk of Court (if you hadn't taken action) would have sent an order to opposing counsel asking for an explanation and/or stating counsel had so many days to submit its brief.  In other words, even if you had not taken action, it is virtually certain the Clerk of Court would have taken action.  It is highly unusual that it would get lost in the system.  Albeit, occasionally the clerk may be delayed in sending the order (as apparently was the situation in your son's case).  Your son  may want to contact the assistant public defender assigned to his case (although he's in prison, he can write to his assigned appellate attorney) to inquire as to the problem and resolution.  It may be there is some underlying problem or situation of which you are not aware.  If not, certainly the assigned attorney can explain what happened and what he/she is doing to make sure the case stays on track at this point.