B757 Captain reported landing safely at destination after experiencing loss of the Right Hydraulic System.

Narrative

Enroute from ZZZ to ZZZ1 at a point minutes from our critical point approaching the fix ZZZZZ on ZZZ2; we received an EICAS caution alert with two messages; R HYD SYS PRESS" and "R HYD QTY" with an immediate reduction in the Right Hydraulic Reservoir from approximately 0.94 to 0.12. In conjunction with this message; we received the overhead light indications for the Right Hydraulic System of; "SYS PRESS;" "RSVR;" "R ENG PRESS;" and "Right ELEC PRESS." Also; on the Status Page of the EICAS Lower Display; we indicated for the Right Hydraulic System a quantity of 0.12 with a pressure of 20 and the RF magenta refill indication. The First Officer was the pilot flying with the right autopilot engaged. Within a few seconds of the system failure; the autopilot disconnected and the First Officer took control of the aircraft manually.We then immediately began to run the QRC checklist for the R Hydraulic System Failure. After completing the checklist up to the deferred items and after selecting the center autopilot; we began the process of communication to the Company and ATC. Since we were unable to communicate via CPDLC / ACARS directly with the Company / ATC; we queried another [Company] flight within our VHF reception range for relay assistance. We were able to pass along our current status to a [Company] aircraft that was behind us on the same track westbound. This communication took several minutes as we requested that they communicate with our Dispatcher and the [Chief Pilot] to assist us in the decision-making on the best airport to continue the flight for subsequent operations as we were operationally safe to continue to ZZZ1 or to divert to ZZZ3; our alternate; if needed. We came to the unified decision of continuing the flight on to our dispatched destination of ZZZ1.Due to the nature of the Right Hydraulic System failure and subsequent loss of some systems including the right autopilot; right manual trim; right thrust reverser; and auto-brakes; along with a possible degradation of flight control effectiveness of the speed brakes; aileron control; and conducting a flaps 20 landing; I made the decision to take control of the aircraft and became the pilot flying and my FO (First Officer) became the pilot monitoring. We also relayed to our Dispatcher to advise ATC that we were [requesting priority handling] and to have the CFR (Crash Fire Rescue) at ZZZ1 standing by for our arrival.Once in VHF range of ZZZ4 Center Control; we checked in with our status. They were already advised of our current situation and gave us subsequent vectors for ZZZ1; clearance for the approach; and landing. We conducted a flaps 20 landing without issue. Once clearing the runway and monitoring all systems; we advised the Tower that all checked good and were given clearance to taxi to our gate. The fire trucks followed us to the gate. When I deplaned; the firefighter took down my information and took notes on the reason for our [situation]."