On January 15, 2003, approximately 1643 Pacific standard time, a Dassault Aviation Falcon 900EX, N11WM, registered to AZAAIR LLC, operated by Pistol Creek Aviation, and crewed by two airline transport rated pilots, encountered moderate turbulence while in cruise at Flight Level (FL) 360, slightly west of HERZO intersection on airway A332 while over the Pacific Ocean en route to Honolulu, Hawaii. The two pilots and three of the four passengers were uninjured, however a fourth passenger, an attendant for one of the other passengers, sustained a broken ankle. The aircraft sustained no damage during the event. The meteorological conditions at the time/altitude of the accident were reported as visual and an IFR flight plan had been filed and activated. The flight, which was personal, was operated under 14 CFR 91, and had originated from Boeing Field, Seattle, Washington, departing at 1226 on the same day. After departure, the aircraft climbed to FL 340 and thereafter, the crew requested FL 360, which was approved. As the flight progressed along airway A332 at FL 360 it encountered intermittent light to occasionally moderate turbulence. A little more than half way into the flight the aircraft's track began to converge obliquely with a cold frontal system extending southwest through the Hawaiian Islands (refer to Attachment FP-I). The crew made repeated requests for a higher altitude through San Francisco Radio but the requests were not approved. Approximately 45 nautical miles south southwest of HERZO (intersection) on A332, the aircraft encountered moderate turbulence for a period of ten seconds or less. The aircraft was operating at FL 360 at the time and had been airborne for approximately 4 hours 17 minutes. The winds aloft chart for FL 340 provided to the crew by Universal Weather showed headwinds of more than 100 knots approximately 30 degrees right of the aircraft's track (refer to Attachment FP-I). The Captain reported that at the time of the turbulence encounter, the aircraft was operating "...right in the tops of clouds with good visibility..." and that "...two of our passengers left their seats to use the lavatory located in the rear of the aircraft..." (the injured passenger was an attendant assisting the non-injured passenger). Following the injury, which was brought to the attention of the crew by a passenger, a request for higher altitude was again requested and then a climb to FL 370 was approved. The aircraft landed uneventfully at Honolulu and the attendant's ankle was x-rayed revealing a fracture condition.