FLC OF A BEECH KING AIR STOPPED CLBING AND DSNDED TO PREVIOUSLY ASSIGNED ALT AFTER ARTCC CTLR QUESTIONED THE ALT TO WHICH THEY WERE ASSIGNED BY DEP CTLR.

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ON MAR/WED/00; AT APPROX XA12 LCL; WE WERE HANDED OFF FROM PHX DEP TO ZAB; AFTER STEP CLBING OUT OF FFZ. LAST ALT WAS 10000 FT; CLRED TO 12000 FT BY PHX AND TURNED OVER TO ABQ. ON CHKING IN I ADVISED OUT OF 10000 FT CLBING TO 12000 FT. ACKNOWLEDGED BY ABQ. SEVERAL SECONDS LATER; AFTER HEARING OTHER RADIO TFC; I THOUGHT I HEARD 'LTT 14000 FT' PARTIALLY BLOCKED ON XMISSION. I READ BACK 'LTT 14000 FT' AND RECEIVED NO RESPONSE; SO WE CONTINUED CLBING TO 14000 FT. A FEW SECONDS LATER THE CTLR CALLED TFC AT 12 O'CLOCK POS AND 1 MI. WE SAW TARGET ON TCASII AT 1-2 MI +700 FT ALT AS WE CLBED THROUGH 13000 FT. WE ADVISED WE WERE IMC; HAD TARGET ON TCASII AND WERE LOOKING FOR TFC. A FEW SECONDS LATER THE CTLR; SOUNDING CONFUSED; ASKED WHAT WAS ASSIGNED. I ANSWERED 14000 FT AND HE SAID THAT WAS FOR ANOTHER ACFT AND TO DSND TO 12000 FT. WE COMPLIED. LATER PHONE CONTACT WITH ARTCC CTLR SUPVR; ZAB; QUALITY ASSURANCE SPECIALIST REVEALED THAT AN OPERROR HAD OCCURRED ON THE CTLR'S PART; WITH A LOSS OF SEPARATION. THEY ARE FILING AN INCIDENT RPT. NO PLTDEV INVOLVED.