Can you appeal a less than honorable discharge after discharge is final?

My son was returning to base and the MO at the gate detected alcohol on his breath. He had a BAL of 0.1. The MO called the police who arrested him for DUI. He was given a general discharge under honorable conditions the day before he went to court for the DUI. At court, it was determined that the evidence was faulty as the breath test given by the MO and the one given by the police were theoretically impossible (son would have had to drink continuously while being held by MO). So, the prosecutor is going to drop the charges. Can he get reinstated into the Navy?