A B737-700 #2 ENG WAS REPLACED AND INADVERTENTLY RELEASED WITH A LOWER THRUST RATED EEC PLUG.

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I RECEIVED A TURNOVER FOR AN ENG CHANGE ON ACFT X. AS WE PROGRESSED THROUGH THE MAINT MANUAL FOR THIS ENG CHANGE; REQUIRES LOOKING AT THE DATA PLATE TO DETERMINE IF THE ENG IS A 24K RATING AND IT ASKS FOR THIS SAME INFO OF THE REMAINING ENG INSTALLED. BOTH ENGS WERE VERIFIED AS 24K ON THE DATA PLATE. AS WE WERE NEARING THE FINAL STEPS TO PERFORM I WAS SIGNING OFF PERFORMED STEPS. WHEN THE MECH IN THE ACFT ASKED THE LEAD MECH ON SHIFT WHAT THE SERIAL NUMBER OF THE ENG INSTALLED WAS; HE GAVE HIM THAT INFO TO PERFORM THE EEC CHK OF LATEST REVISED SOFTWARE; SO WE ASSUMED HE HAD ALSO CHKED THE IDENT/CONFIGN PAGE IN THE CDU. WE SIGNED THE STEP ON PAGE XX AND PROCEEDED TO THE RUN-UP AREA TO PERFORM A REQUIRED 65% PWR ASSURANCE RUN. NEITHER I; OR THE LEAD MECH WERE AWARE OF ANY 22K ENGS IN OUR INVENTORY. SUGGESTIONS FOR FUTURE: IF THEY COME INTO OUR ENG SHOP INCLUDE STEP FOR CHKING THE THRUST RATING PLUG. IF WE ARE RECEIVING THE ENG AS A LOANER FROM ANOTHER FACILITY; INCLUDE A SCREEN IN THE RECEIVING PROCESS TO ALERT THE RECEIVING INSPECTION AT THIS TIME. SUPPLEMENTAL INFO FROM ACN 766618: MY CREW TOOK OVER THE #2 ENG CHANGE ON ACFT X. AS THEY WERE PREPARING TO PUSH OUT AND DO THE LEAK CHKS AND OPS CHKS; I WAS TAKING CARE OF THE PAPERWORK. I SAW ON THE 2ND PAGE OF THE MAINT MANUAL THAT BOTH ENGS WERE 24K RATED. MECH (PERSON #3) WAS IN THE R SEAT AND ASKED ME FOR THE ENG SERIAL NUMBER SO HE COULD CHK THE EEC DATA; I GAVE IT TO HIM; HE TOLD ME IT WAS ALL GOOD. I ASSUMED HE ALSO CHKED THE ENG IDENT CONFIGN SCREEN; SO I SIGNED FOR IT AND TOLD MY INSPECTOR IT WAS GOOD. WE ARE NOT SUPPOSED TO HAVE ANY 22K ENGS IN OUR SYS. THE MANUAL ONLY REQUIRES A 65% PWR ASSURANCE RUN; NOT TKOF PWR; WHICH WOULD HAVE SHOWN US WE HAD A PROB. CALLBACK CONVERSATION WITH RPTR ON ACN 766613 REVEALED THE FOLLOWING INFO: REPORTER STATED THE COCKPIT MECHANIC DID VERIFY THE INSTALLED #2 ENGINE SERIAL NUMBER MATCHED THE INFO IN THEIR ONBOARD CDU. THE THRUST RATING PLUG ON THE EEC UNIT HOWEVER; WAS NOT CROSS-CHECKED WITH THE COCKPIT MECH; TO CONFIRM THE CORRECT THRUST RATING FOR THIS ENGINE WAS VERIFIED IN THE ACFT'S CDU IDENT CONFIGURATION SCREEN. THE PROBLEM SURFACED APPROX THREE DAYS AFTER THE ENGINE CHANGE WHEN T/O SPOOL-UP TARGETS COULD NOT BE MET AT A WARMER TEMPERATURE AIRPORT. REPORTER ALSO ADDS THIS WAS A BORROWED (LOANER) ENGINE AND HIS COMPANY'S RECEIVING PROCESS ALSO MISSED IDENTIFYING THE LOWER THRUST RATED EEC PLUG. THE ENGINE DATA PLATE SHOWED 24;000 # THRUST.