What was found
CREW WAS FLYING IN CRUISE AND CROSSFEEDING FUEL FROM THE RIGHT TO THE LEFT TO CORRECT A FUEL IMBALANCE (R WING HEAVY). CREW WAS THEN INSTRUCTED BY ATC TO CLIMB; AT THIS POINT TOTAL FUEL WAS APPROX 950 LB (555 LB IN THE RIGHT WING, 395 LB IN THE LEFT WING). CREW ADVANCED THE THROTTLES TO MCT SETTING AND PITCHED UP FOR THE CLIMB. APPROXIMATELY 1 MIN 40 SEC LATER, THE L FUEL FEED CAS WARNING MESSAGE POSTED TO INDICATE A LESS THAN FULL L HOPPER TANK. THE CREW IMMEDIATELY REDUCED PITCH ANGLE AND STOPPED THE FUEL CROSSFEED, AND THE FUEL FEED WARNING EXTINGUISHED. UPON FURTHER INVESTIGATION, IT WAS FOUND THAT DURING CERTIFICATION TESTING OF THE SJ30-2, THE SAME CONDITION WAS EXPERIENCED (HOPPER TANK FUEL DIMINISHED WHILE CROSSFEEDING WITH LOW FUEL AND AT HIGH THRUST SETTING). THE SJ30-2 CERTIFICATION TEST RESULTS REPORT RECOMMENDED AN AIRCRAFT-LEVEL AFM LIMITATION TO AVOID CROSSFEEDING WITH FUEL QUANTITY BELOW 930 LB, BUT SUCH A LIMITATION WAS NEVER IMPLEMENTED. THE CURRENT FLIGHT CREW BELIEVES THAT THIS WAS AN OVERSIGHT, AND BASED ON THEIR EXPERIENCE WITH THIS EVENT THAT A NOTE IN THE AFM, DESCRIPTION IN THE PILOT TRAINING CURRICULUM, AND POTENTIALLY A PLACARD SHOULD BE ADDED.