B777-200 FLYING OVERWATER IN CLASS II AIRSPACE; INDICATED LOW HYD QUANTITY IN LEFT SYSTEM. FLT CREW RETURNED AND DECLARED EMER FOR APCH AND LNDG.

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DURING CRUISE WITH RELIEF CREWS ALREADY ON REST BREAK; A HYD QUANTITY L MESSAGE APPEARED. FLUID LEVEL INDICATED 0.35%. WE IMMEDIATELY CONTACTED COMPANY MAINT VIA DISPATCH AND ELECTED TO TURN OFF THE L HYD PUMPS TO CONSERVE FLUID. IN CONSULTATION WITH DISPATCH AND MAINT; A DECISION WAS MADE TO DIVERT TO ZZZ. A REQUEST FOR CLRNC DIRECT TO ZZZ WAS MADE VIA HF AND EVENTUALLY CONFIRMED VIA VHF WITH ZZZ1 CTR. NO EMER WAS DECLARED AT THIS TIME; AS WE ANTICIPATED BEING ABLE TO REPOWER THE L HYD SYS WITH THE REMAINING FLUID PRIOR TO LNDG. MAINT CONCURRED. WHILE ENRTE TO ZZZ WE CONTINUOUSLY MONITORED THE HYD QUANTITY; AND NOTICED A SLOW BUT STEADY DECREASE IN QUANTITY DESPITE THE PUMPS BEING TURNED OFF. THE CTR AND R SYS OPERATED NORMALLY. WHEN OUR COMPUTATIONS INDICATED THAT WE MIGHT NOT HAVE ENOUGH TIME TO ARRIVE IN ZZZ BEFORE THE L HYD QUANTITY REACHED A LEVEL THAT COULD PRECLUDE REGAINING NORMAL PWR TO THE SYS; WE DECLARED AN EMER WITH ZZZ CTR. MEN AND EQUIP WERE STANDING BY; AND WE MADE A NORMAL APCH; LNDG; AND TAXI TO THE GATE WITH THE L HYD SYS SHUT DOWN. L HYD SYS QUANTITY REACHED ZERO JUST PRIOR TO LNDG. CTR AND R SYS REMAINED NORMAL.