What was found
ON AUG19TH, AE 857 FLIGHT (A/C B-16802, S/N 28236) EXPERIENCED THAT "SPEED TRIM FAIL" LIGHT CAME ON DURING CLIMBED THROUGH 2500 FEET. BY 10 SECONDS, THE LIGHT WENT OFF. WHILE CLIMBED THROUGH 5000 FEET AND THE CREW ENGAGED THE "AUTO-PILOT", THE "STAB OUT OF TRIM" WARNING LIGHT CAME ON. THE CREW FOLLOWED QRH PROCEDURE, AND FOUND THAT THE CONDITION REMAINED UNCHANGED. DUE TO THE ROUTE NEED RNP AND RVSM OPERATION, IT HAD TO HAVE "AUTO-PILOT". IF NOT, THE CRUISE HEIGHT HAD TO DESCENT BELOW FL290. CONSIDERATION OF FUEL QUANTITY IN THAT SITUATION, THE CREW ASK ATC FOR AIR TURNED BACK TO CKS AIRPORT. AIRCRAFT LANDED SAFELY. IAW AMM PART 2 27-41-71, REPLACED STAB TRIM MOTOR. FUNCTION CHECK NORMAL. PER AMM 22-11-8