LTSS BTWN AN FA22 TRAINING FLT AND A B390 WHEN THE FA22 DSNDED BELOW ASSIGNED ALT. THE FA22 HAD BEEN ISSUED ON THE BE90.

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I WAS THE INSTRUCTOR PLT IN THE FA22 ON A COMPANY TRAINING FLT. THE TRAINEE WAS FLYING UNDER THE HOOD. WE WERE CRUISING AT 6000 FT MSL AND HAD ASKED CTR FOR AN APCH INTO GVT; TX. CTR INSTRUCTED US TO FLY PRESENT HDG TO INTERCEPT THE 170 DEG RADIAL OFF BLUE RIDGE VOR. WE WERE TOLD TO INTERCEPT THE 9 DME ARC AND CLRED FOR THE APCH (VOR/DME-A) AT GVT. ABOUT 4 MI SHORT OF INTERCEPTING THE 9 MI ARC; I GAVE THE TRAINEE A SIMULATED PRESSURIZATION EMER. HE WAS WORKING OUT THE EMER AS CTR CALLED OUT TFC; A KING AIR AT 1-2 O'CLOCK AND 5000 FT. WE REPLIED WITH 'LOOKING' AND I SCANNED FOR THE TFC. THE TRAINEE NOW HAD THE SIMULATED EMER PROB UNDER CTL AND INTERCEPTING THE ARC. AS I SCANNED FOR TFC AND CHKED TO SEE THAT THE SIMULATED EMER WAS TAKEN CARE OF PROPERLY THE CTR SAID SAY ALT. THE TRAINEE RESPONDED WITH 5500 FT DSNDING TO 2200 FT. THE CTR SAID MAINTAIN PRESENT ALT OR CLB AND MAINTAIN 6000 FT. WE STOPPED OUR DSCNT AND CLBED BACK TO 6000 FT. WE WERE THEN NOTIFIED OF A POSSIBLE ALTDEV; POSSIBLE LOSS OF SEPARATION; AND TOLD TO CONTACT ZFW UPON LNDG. WE UNDERSTOOD WE WERE CLRED FOR THE APCH AND DID NOT REALIZE WE WERE PLACING THE ACFT IN JEOPARDY WITH ANOTHER. UPON SPEAKING TO ATC AFTER THE FLT; THEY INFORMED US THE LOSS OF SEPARATION RESULTED IN A PROX BTWN OUR ACFT AND THE KING AIR OF POSSIBLY 1.1 - 1.5 NM HORIZ AND POSSIBLY 300 FT VERT. NEITHER ACFT HAD VISUAL CONTACT.