A BE40 was unable to maintain FL430 notwithstanding the aircraft performance data showing the altitude to be a fuel efficient option. The flight crew initiated an emergency descent to avoid a high altitude stall.

Narrative

In an attempt to reduce fuel consumption and in accordance with the AFM and POM; we requested a climb to FL430 and; after receiving clearance; initiated a climb to that flight level. According to both the Aircraft Flight Manual (AFM) and Pilot Operating Manual (POM); at the aircrafts current weight of 15;000 and an SAT of ISA -5; the aircraft should have been capable of climbing to FL450.While climbing the airspeed diminished only slightly and the AOA (Angle of Attack) only showed moderate increase; what one would expect in a climb. After leveling at FL430; the airspeed began to degrade rapidly along with a rapid increase in AOA. We requested an immediate descent to FL400. ATC informed us that there was a Falcon at our 4 o'clock position and that we would have to wait for proper separation. Both my co-pilot and I had visual contact with the Falcon and began an immediate descent to counter the impending stall. We immediately contacted ATC again and told them that we could not maintain FL430 and had started a descent and also advised them that we had visual contact with the falcon.Following an additional review of the AFM and POM; there is no reason the aircraft; should not have been able to climb to and maintain FL430 at that time. The AOA only began to increase and the airspeed only began to diminish rapidly after leveling off at FL430.