B787 Captain reported moderate mountain wave with subsequent altitude and airspeed gains and losses.

Narrative

FL390; B787-9; Cruise; in the clear above cloud layerWhile in cruise at FL390 approximately 30 NM northeast of City X; the flight encountered moderate mountain wave activity. Airspeed began to increase rapidly. The speedbrake was deployed; however; airspeed continued to increase; and the aircraft began an uncommanded climb to approximately FL39700.An overspeed warning (aural and EICAS OVERSPEED message) was received. The aircraft subsequently descended back toward FL390 as airspeed decreased; but the autopilot was unable to maintain altitude; and the aircraft further descended to FL38600 as airspeed continued to decay.ATC was advised that we were unable to maintain FL390; and a descent was requested and approved to FL370. The flight stabilized at FL370 without further incident.The Flight Attendants were notified of moderate turbulence procedures are in effect" and a PA to the passengers (and crew in the bunks) was made to require them to remain seated with seatbelts secured.Flight Deck Wi-Fi was unavailable; preventing in-flight weather updates. Dispatch sent a SIGMET for turbulence and wind shear via ACARS along with an earlier PIREP for turbulence.Prior to departure from ZZZZ; the flight plan was loaded; however; without internet connectivity; no real-time turbulence or mountain-wave data was available during cruise.Cause: Moderate mountain wave activity caused transient overspeed and altitude deviations beyond autopilot control limits. Coordination with ATC was timely; and the flight remained under control throughout. Lack of real-time en-route weather data contributed to limited situational awareness of mountain-wave activity along the route. We need better Flight Deck Wi-Fi reliability on the B-787"