Falcon 20 flight crew reported fuel leak inflight causing inflight engine shutdown. The flight continued and landed without incident.

Narrative

Second overwing top off was performed to ensure adequate fuel load for flight leg between ZZZ and ZZZ1. Planned fuel burn was 6300lbs. 45min. Reserve was 1500lbs. Total fuel load was approx. 8200lbs.Once established in cruise flight at FL340; the Cruise Checklist directed a fuel quantity check which revealed a fuel imbalance showing the right wing tank with a lower quantity.Fuel flow and burns were equal. We initially suspected an inaccurate gauge and began troubleshooting that perceived problem; checking circuit breakers and inverters. The right quantity continued to drop. We began to suspect a leak somewhere in the system and started to plan for a possible diversion along our route of flight.As we were deciding that; our destination airport provided as near and suitable landing surface as any others; low pressure warning lights began to illuminate which prompted us to respond by addressing and following the Abnormal Checklist for each warning. One exception was to not open the cross feed thereby preventing any loss of left tank quantity through a leak. Shortly thereafter; the right engine shutdown. We then completed the appropriate Abnormal Checklist and secured the right engine; advised ATC of our one-engine status and of the need to proceed direct to ZZZ1 immediately with no delay for landing. Descent; approach and landing were completed with no further problems. Company ops was then contacted and apprised of the situation. The investigation is ongoing to determine cause and corrective action.