I would not apply again its not going to change the status , I would have him get more info about his crime, what county it was in and get with the county sheriff of the county the supposed crime happened in AZ and have them send certified papers of a clean record directly to Springfield to whom ever is working on his FOID stuff which you will need to find out who that is .
I have a CDL / Hazmat driver here at work for me , I got a letter saying that he had been convicted of use of narcotics / intoxication while driving and his CDL had been revoked . This is a 69 yr old man thats never touched dope . LOL just a big mistake that took us several weeks to get corrected , come to find out it was a guy with the exact name that was 24 yrs old . Now how do you mix that up ? It happens .
If you do as stated as above and dont get results then I would get a attorney involved as they obviously have something wrong on his record that needs corrected that may have adverse effects in the future