As far as we can tell, you are not required to notify the Department of Justice of an arrest or conviction. But the DOJ will revoke a license if the license holder is no longer legally eligible to possess a concealed weapon. They will also suspend a license if a court has prohibited a license holder from possessing a dangerous weapon as a condition of bail.
If your license is suspended or revoked, you will receive a notice in the mail within one day of the revocation or suspension and takes effect when you receive it.
Within seven days, you must deliver the license to the DOJ, mail the license via certified mail, or mail a signed statement stating you no longer have possession of it and the reason why. Failing to do so can result in a fine of up to $500 and 30 days in jail.