ACR X UNAUTHORIZED CLB THROUGH OCCUPIED ALT. READBACK WRONG ALT LTSS FROM ACR Y. SYS ERROR.

Narrative

WE WERE ON A SCHEDULED FLT FROM LAX TO MMH. AS WE DEPARTED LAX; THE TWR CTLR HANDED US OVER TO DEP CTL. WE CONTACTED DEP ON 125.2 AND CALLED ACR X OUT OF 1000 FOR 2000. CTLR RESPONDED WITH 'ROGER.' WE LEVELED AT 2000 AND STAYED THERE FOR APPROX 2 MIN WHEN THE SAME VOICE CAME BACK AND SAID; 'ACR X DID YOU CHK IN?' WE RESPONDED; 'YES; WE'RE LEVEL 2000.' THE CTLR RESPONDED; 'ROGER CLB AND MAINTAIN 4000.' WE LEVELED AT 4000 JUST INSIDE THE CLOUDS. THE NEXT CALL FROM DEP WAS 'ACR X TURN R HDG 360; MAINTAIN 6000.' WE TURNED AND BEGAN OUR CLB. OUT OF 5000 THE CTLR ASKED OUR ALT. WE SAID OUT OF 5 FOR 6000. THE CTLR SAID; 'EXPEDITE THROUGH 6000; TFC 12 O'CLOCK; 2 MI AN ACR Y; LTT.' HE WAS IN SIGHT AND WAS NO FACTOR. WE TOLD ATC WE HAD HIM IN SIGHT; AT WHICH TIME HE SAID 'I DON'T KNOW WHAT YOU READ BACK; BUT YOU WERE ASSIGNED 4000.' MY FIRST QUESTION TO MYSELF WAS; WHY DID HE NOT KNOW WHAT WE READ BACK. IT IS AS IMPORTANT FOR HIM TO KNOW WHAT WE READ BACK AS IT IS FOR US TO KNOW WHAT WE WERE ASSIGNED. WE DID NOT QUESTION THE ALT ASSIGNED AS IT WAS APPROPRIATE FOR OUR LOCATION. THE CAPT AND I DISCUSSED WHAT OCCURRED AND KNOW HE SAID 6000. UNFORTUNATELY; WITH HIM NOT HEARING THE READBACK; A CONFLICT OCCURRED. WE HAVE HEARD NOTHING ELSE FROM ATC EXCEPT WHAT IS IN THIS RPT.