SAT TRACON Controller reported being advised of an NMAC from an aircraft operating in SUA with an untracked VFR aircraft resulting in the aircraft taking evasive action to avoid a possible collision.

Narrative

Aircraft X was on an IFR flight plan established in area 6L of the RND1B MOA. Aircraft X inquired if I had traffic for them which I replied I did not because there was nothing observed on RADAR. Aircraft X said he had a near mid air during aerobatic maneuvers with a small single engine aircraft flying northbound at 8;500. During the discussion of this event on frequency with Aircraft X; a primary target did appear intermittently after the event about 2 miles north of Aircraft X. Upon review of playback there was no observed RADAR target; primary or secondary at all until after the NMAC had occurred. I called the next two sectors and that the primary target was heading for and gave them a reported altitude. Aircraft X reported the event to be a near mid air with zero lateral and less than 500 feet vertical as they aborted their maneuver to avoid the aircraft. Recommendation - Aircraft with zero transponders should not be allowed to fly through SUA. This aircraft was invisible to RADAR and TCAS/ADSB flying right into the flight pattern of aircraft doing military training. The fact that this is perfectly legal is unacceptable.