A VFR GA CESSNA PLT VIOLATED MIA CLASS B AIRSPACE; FLEW IN IMC; AND HAD AN NMAC WITH A B737-200.

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AFTER A MISSED APCH; I WAS GETTING VECTORS AROUND THE ARPT WHILE WAITING FOR WX TO IMPROVE AND TO COORDINATE POSSIBLE DIVERSION. WHILE IN AND OUT OF THE CLOUDS; MIAMI APCH ISSUED AN ADVISORY OF TFC (Y) AT 10 O'CLOCK POS; AT 2000 FT MSL. SEVERAL ADVISORIES FOLLOWED. WE DID NOT GET A CLRNC TO CLB FROM APCH CTL. AS I WAS ABOUT TO CLB; HE (Y) TURNED HIS XPONDER OFF; SINCE HE DISAPPEARED FROM OUR TCASII AND APCH LOST HIM ELECTRONICALLY. ASSUMING THAT HE (Y) HAD TO HAVE SEEN US (SINCE HE TURNED THE XPONDER OFF); I ASSUMED THAT HE HAD TO BE EXECUTING AN EVASIVE MANEUVER (PROBABLY; TURNING AND CLBING). CONSEQUENTLY; I ELECTED TO HOLD ALT. FROM A BREAK IN THE CLOUDS OFF TO MY L; I SAW A HIGH-WING; SINGLE ENG ACFT (PROBABLY A CESSNA); BANKING L AND CLBING AWAY FROM HIS COURSE INTO MY ACFT. I SAW THE FACE OF THE PLT. I NOTIFIED APCH CTL OF THE INCIDENT AND ASKED THEM TO TRACK THE ACFT UNTIL LNDG; WHICH THEY DID. AFTER LNDG; I TALKED WITH THE APCH CTL SUPVR AND INFORMED HIM THAT THE CULPRIT ACFT; NOT IN COMS WITH ATC; WAS FLYING IN REAL IFR CONDITIONS. I INFORMED HIM OF MY INTENTIONS TO FILE A RPT.