NMAC; SEE AND AVOID.

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YOUR RPTR HAD DEPARTED COI FOR A VFR FLT TO OMN TO DROP OFF A PAX. YOUR RPTR WAS MAKING A SLOW CLB TO 2500 FT MSL. NO VFR RADAR SVC HAD BEEN REQUESTED BUT PAFB RAPCON WAS BEING MONITORED. WHILE E OF TIX A COM BTWN PAFB RAPCON AND OUR AEROSTAR; ALSO VFR NBOUND OUT OF COI WAS OVERHEARD. PAFB RAPCON RPTED TO THE AEROSTAR TFC ALSO NBOUND AT 12 O'CLOCK AND 1800 FT. THE AEROSTAR PLT RPTED THAT HE HAD THIS TFC IN SIGHT. YOUR RPTR AT THAT TIME WAS AT 1800 FT AND BELIEVED THAT THE TFC IDENTED BY PAFB RAPCON TO THE AEROSTAR PLT WAS YOUR RPTR'S ACFT. YOUR RPTR CONTINUED TO CLB VERY GRADUALLY AND WAS NOT ABLE TO SEE THE OVERTAKING TFC WHICH WAS BEHIND AND ABOVE AT 2500 FT RPTED ALT. APPROX 2-3 MINS LATER WHILE E OF X21 THIS RPTR'S ACFT WAS CLBING THROUGH 2350 FT AND WAS PASSED DIRECTLY OVERHEAD BY THE AEROSTAR AT AN ESTIMATED 100 PLUS OR MINUS FT OF VERT SEPARATION. NO EVASIVE ACTION WAS TAKEN BY YOUR RPTR NOR DID THE AEROSTAR APPEAR TO HAVE TAKEN ANY EVASIVE ACTION. YOUR RPTR QUESTIONED MY PAX FOR THEIR ESTIMATE OF THE VERT SEPARATION AND THEY CONFIRMED THEIR ESTIMATE AS 100 FT OR SO. YOUR RPTR THEN MADE A RADIO CALL TO PAFB RAPCON TO RPT THE INCIDENT AND ADVISED THE 100 PLUS OR MINUS FT NEAR MISS. PAFB RAPCON CONTACTED THE AEROSTAR PLT WHO SAID HE PASSED 400 FT OVERHEAD. YOUR RPTR RESPONDED TO THIS BY AFFIRMING THE 100 FT DISTANCE. YOUR RPTR BELIEVES THE AEROSTAR PLT DID NOT MAINTAIN VISUAL CONTACT WITH THE RPTED TFC AND ASSUMED HE WOULD PASS CLR OVERHEAD. PAFB RAPCON; ALTHOUGH NOT TECHNICALLY FURTHER RESPONSIBLE; DID NOT ADVISE THE AEROSTAR FURTHER OF THE POTENTIAL CONFLICT AND IN PARTICULAR THE ALT CLOSURE BY THE RPTED TFC. YOUR RPTR 'ASSUMED' THE AEROSTAR WOULD MAINTAIN ADEQUATE VISUAL SEPARATION AND CONTINUED TO CLB WITHOUT THE AEROSTAR BEING IN SIGHT.