ZAB CTLR DESCRIBED CONFLICT EVENT AT FL350 WITH ACFT UNDER ZKC CTL; ALLEGING; DE-CONFLICTION COORD WAS COMPLETED BUT ACTIONS NOT TAKEN.

Narrative

HVY TSTMS THROUGHOUT THE EVENING; WITH MODERATE TO SEVERE TURB RPTED FL370 AND ABOVE. NUMEROUS DEVS AROUND WX; CAUSING MANY CONFLICTIONS. STAFFING AT ZAB WAS NOT SUFFICIENT; MOST CTLRS WERE TIRED AND NOT RECEIVING APPROPRIATE BREAKS TO ENSURE THEY WERE RESTED AND ABLE TO HANDLE THE HVY VOLUME OF TFC. TRAINING WAS OCCURRING ON THE D-SIDE OR ASSIST POS. THE CRJ9 WAS BEING CTLED BY ME HDG NE TOWARDS GAG AT FL350. THE A320 WAS BEING CTLED BY ZKC ALSO AT FL350 HEADING TOWARDS THE SE. AFTER RECOGNIZING THAT THERE WAS A CONFLICTION; THE D-SIDE INSTRUCTOR COORD WITH ZKC TO DECONFLICT THE 2 ACFT. ZKC SAID THAT THEY WOULD CLB THE A320 TO FL360. ZKC NEVER CLBED THEIR ACFT CAUSING THE TWO TO COME VERY CLOSE. I INITIATED A 60 DEG TURN AND ISSUED AN IMMEDIATE CLB TO FL360; THE PLT COMPLIED WITH THE INSTRUCTIONS IN A VERY TIMELY MANNER DE-CONFLICTING THE ACFT. BECAUSE ZKC DID NOT FOLLOW THROUGH WITH THEIR INITIAL PLAN; MY CTL INSTRUCTIONS PLACED THE CRJ9 IN CLOSE PROX TO THE TSTM. LOW STAFFING; FATIGUE; WX; AND TRAINING ALL PLAYED MAJOR ROLES IN THE INCIDENT.