AN ACFT HAD DIFFICULTIES PICKING UP AN IFR CLRNC; WITH A CLRNC VOID TIME; AT A CLASS G ARPT. IFR CLRNC IS FINALLY RECEIVED BY CELLULAR PHONE.

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DURING DEP SEQUENCE OF OUR MISSION FROM GPT; THE CTL TWR CLOSED. WE WERE ADVISED BY THE TWR CTLR BEFORE HE SHUT DOWN OPS TO CONTACT GREENWOOD RADIO FOR OUR ATC CLRNC TO LAX ON 122.1; THEN LISTEN ON THE GPT VOR FREQ 109.0 COPY THE CLRNC. WE WERE UNABLE TO GET GREENWOOD RADIO ON ANY FREQ; AND I ASKED THE FO TO ATTEMPT CONTACT WITH ANY VHF FREQ FOR NEARBY KEESLER AFB AS A POSSIBLE RELAY. THAT TOO FAILED SO WE ATTEMPTED TO USE THE CTAF FOR A RELAY TO ZHU. THAT ALSO FAILED. SINCE WE STILL HAD OUR GND HANDLER ABOARD THE ACFT; I ASKED THE FO TO GET HIS CELL PHONE AND CALL GREENWOOD. HE DID THAT; PUT OUR CLRNC ON REQUEST; AND I WATCHED HIM COPY THE CLRNC ON OUR COMPUTER FLT PLAN. SINCE WE HAD TO RESORT TO CELL PHONE USE; NEITHER THE FE NOR MYSELF WAS ABLE TO LISTEN TO THE GREENWOOD RADIO OPERATOR READ THE CLRNC FROM HOUSTON. WE WERE CLRED AS FILED TO MAINTAIN 4000 FT; EXPECT FL350 WITHIN 10 MINS; SQUAWK XYZW; CLRNC VOID TIME XA45; CONTACT HOUSTON 127.65 ONCE AIRBORNE. THE WX WAS VFR AND I SAW NO CONFLICT WITH THE ARRIVING ACFT; THE FO USED CTAF PROCS TO ADVISE OUR DEP AND I NOTED THE TIME AS XA43. AFTER DEP; WE CONTACTED HOUSTON AND THE CTLR ADVISED US THAT WE HAD MADE A PLTDEV BECAUSE OUR CLRNC VOID TIME WAS XA40 AND TO CALL A PHONE NUMBER ON ARR AT LAX. WE WERE PRETTY BUSY DOING OUR CLB CHKS AND I ADVISED HOUSTON THAT OUR CLRNC VOID TIME WAS XA45; NOT XA40 AND I ASKED HOUSTON TO STAND BY. ABOUT 7 MINS PASSED AS WE RAN OUR CHKLISTS; THE HOUSTON CTLR ADVISED ME TO CANCEL THE TELEPHONE REQUEST BECAUSE THE ARRIVING COMMUTER ACFT HAD CANCELED HIS IFR CLRNC PRIOR TO OUR DEP.