B777-300 flight crew reported a loss of hydraulic fluid in flight and a diversion to a suitable airport for a safe landing.

Narrative

Aircraft had a right hydraulic LF condition arriving in ZZZZ1. Maintenance blocked right reverser and topped off fluid. Approximately 9 hours into the flight; aircraft displayed HYDRAULIC Fluid low Rt. There was 39% fluid remaining with a loss rate of about .01 per 10 min. We determined the loss rate would not allow continued flight into oceanic airspace. Consulted with Dispatch and Maintenance Control for the best diversion airport. Maintenance Control cautioned do not let the hydraulic pumps run dry as it could cause a fire. We [requested priority handling] and received clearance directly to ZZZZ. Although low pressure had not developed on the right hydraulic system yet; after consulting with the crew; I elected to turn off the pumps to retain as much fluid as possible. We briefed loss of right hydraulic conditions for the landing. With 37% fluid remaining; on final approach; pumps were switched on for a normal landing. ZZZZ safety checked aircraft after landing; finding no issues we taxied to the gate.Cause: As pilot in command (PIC) I made the decision to turn off the pumps before low pressure developed. I felt this action provided the best margin of safety to compete the flight.