PLT DEPARTING DFW IN HS125 BELIEVES THE DEP CTLR MAY HAVE INADVERTENTLY ISSUED AN INCORRECT ALT.

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I WAS A REQUIRED CREW MEMBER DURING A CFR 14 PART 91 FLT FROM ADS TO AMS IN ACFT X (A HAWKER HS125-700) ACFT OPERATED BY OUR COMPANY ON SEP/XA/00. THE FLT WAS ON AN IFR FLT PLAN TRANSITION. TKOF WAS CONDUCTED NORMALLY AND INITIAL ALT AND HDG ASSIGNMENTS WERE AN IMMEDIATE L TURN TO HDG 100 DEGS; AND INITIAL CLB TO 2000 FT MSL. WE WERE TO RECEIVE VECTORS FOR THE ASSIGNED DEP PROC. WE WERE SUBSEQUENTLY ASSIGNED A SBOUND HDG AND ASSIGNED A HIGHER ALT OF 8000 FT MSL; AFTER WHICH WE WERE HANDED OFF TO THE NEXT TRACON CTLR. SHORTLY AFTER THE HDOF; THIS CTLR INSTRUCTED US TO CLB AND MAINTAIN 13000 FT MSL. THE PNF READ BACK THE ALT ASSIGNMENT; LOOKED AT ME AND SAID CLB TO 13000 FT MSL AND SET THAT ALT IN OUR ALT SELECTOR. THE CTLR DID NOT ACKNOWLEDGE. WE BEGAN OUR ASCENT TO 13000 FT MSL; AFTER CONFIRMING TO EACH OTHER AND THE CTLR THAT 13000 FT MSL WAS THE ASSIGNED ALT. UPON PASSING 11500 FT MSL; THE CTLR ADVISED US THAT HE BELIEVED TO HAVE ONLY CLRED US TO 10000 FT MSL. WE WERE INSTRUCTED TO EXPEDITE OUR CLB TO 13000 FT MSL TO RESOLVE AN IMPENDING TFC CONFLICT WITH ACR Y; AN F100. WE COMPLIED QUICKLY AND TFC PASSED BELOW US WITH 1000 FT SEPARATION. WE TOLD THE CTLR DURING OUR CLB TO 13000 FT THAT WE WERE ASSIGNED 13000 FT MSL. THE CTLR DID NOT REPLY. SHORTLY THEREAFTER; WE WERE HANDED OFF TO ZFW; AND NO FURTHER MENTION OF THE INCIDENT WAS MADE TO US. THE FLT PROCEEDED TO DEST UNEVENTFULLY. THAT MORNING; THE CTLR APPEARED BUSY AND DID NOT CORRECT HIMSELF FOR HIS ERRONEOUS ALT ASSIGNMENT WHEN WE READ IT BACK TO HIM. THE FLC PERFORMED ALL TASKS WITH PROPER EXECUTION OF CRM. THE CTLR COULD HAVE AVOIDED THE WHOLE INCIDENT IF HE HAD PAID ATTN TO PLT READBACKS OF ALT ASSIGNMENTS.