FLC OF LR35 ON A PROVING FLT FOR PART 135 CERTIFICATION HAS LOSS OF RADIO CONTACT AND LTSS WITH AN ACR ALSO WITH NO CONTACT.

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DEPARTED FROM FTY ON AN IFR FLT PLAN TO STL WITH 4 FAA INSPECTORS ON BOARD CONDUCTING PROVING RUNS TO PUT A LEAR JET ON A PART 135 CERTIFICATE. WE WERE CRUISING AT FL350 AND WERE SUBSEQUENTLY DSNDED TO FL240 ON THE ARR INTO STL. DURING THE DSCNT TO FL240 WE WERE GIVEN A FREQ CHANGE; WHICH WE ACCOMPLISHED AND RPTED IN AT FL240. THERE WERE NO INSTRUCTIONS TO DSND TO A LOWER ALT AND WE WERE GETTING CLOSER TO OUR DEST AND NEEDED TO DSND. AFTER SEVERAL ATTEMPTS TO CONTACT CTR; WE FINALLY CONTACTED STL APCH AND THEY GAVE US A CTR FREQ TO CONTACT; WHICH WE DID. UPON CONTACTING THE CTR ON THE FREQ GIVEN US BY STL; WE WERE ASKED WHERE WE HAD BEEN. WE EXPLAINED OUR SIT AND WE WERE TOLD WE WERE INVOLVED IN AN INCIDENT WITH AN ACR ACFT THAT THEY (THE CTR) WERE ALSO UNABLE TO COMMUNICATE WITH AND THAT WE HAD PASSED WITHIN 4 MI OF SAID ACFT AT THE SAME ALT. WE WERE ASKED SEVERAL QUESTIONS BY THE CTR AND WE TRIED TO EXPLAIN WHAT HAPPENED. SO IN ORDER TO ELIMINATE FREQ CONGESTION WE ASKED FOR A PHONE NUMBER TO CALL ONCE WE WERE ON THE GND. WE THEN DIVERTED TO SUS AS PER THE SCENARIO PRESENTED TO US BY THE FAA INSPECTORS ON BOARD THE ACFT. ONCE ON THE GND AT SUS; I CONTACTED MR X; GATEWAY SUPVR; AND DISCUSSED THE SIT WITH HIM AT LENGTH. THE CONVERSATION ENDED WITH THE UNDERSTANDING THAT AN INVESTIGATION WOULD BE FORTHCOMING. MY NAME AND TELEPHONE NUMBER AND THE FAA INSPECTOR'S NAME AND TELEPHONE NUMBER WAS GIVEN TO MR X AT THE END OF OUR CONVERSATION. I DO NOT KNOW WHAT FACTORS WERE INVOLVED OTHER THAN WE WERE FOLLOWING INSTRUCTIONS FROM CTR AND WORKING A SCENARIO FROM THE FAA PERSONNEL ON BOARD THE ACFT IN CONJUNCTION WITH THE PROVING RUNS.