Air carrier Captain reported encountering GPS jamming in the vicinity of MUO Air Force Base that resulted in loss of the left GPS even after exiting the area of jamming.

Narrative

I was the flying pilot for the leg but had just started break and fell asleep quickly. Upon return to flight deck the First Officer (F/Os) related the incident. Just prior to entering ZLC (Salt Lake Center) they noted an ATC EICAS w/transponder fail light. Confirming the situation they noted both GPS positions blank in the FMC prog" pages resulting in an ADS B failure prompting the EICAS. ATC reported GPS jamming; all aircraft in a wide area experiencing it. ATC speculated it was from MUO Mt. Home; AFB. Jamming lasted around 2 hours; then the R GPS recovered; and the crew noted a L GPS EICAS. Phone patch to Dispatch and Maintenance yielded negative recovery of L GPS. All 3 IRS systems were never impacted and it was agreed to continue; enter Class II airspace with 1 GPS and 3 IRS.Due to the weather in HNL we were expecting a 26L landing which only has an RNAV (RNP) and LDA. Upon my return to the flight deck the crew briefed me on the situation; I stated that I used to fly this fleet with only 3 IRSs before GPS; and I appreciated them continuing into Oceanic airspace. They also briefed me upon review of the Runway 26L approaches they discovered the RNAV (RNP) required 2 GPS and so we were limited to the LDA approach with higher minimums. This was a concern as the HNL forecast was acceptable but not great and PHOG/OGG; the alternate would require an RNAV (GPS) approach due to Cruise weather. I checked PHKO/KOA forecast which was VMC and advised Dispatch this would be the preferred 2nd alternate if HNL and OGG deteriorated. Dispatch responded with time and fuel to KOA for planning purposes. Uneventful approach [and] landing completed into HNL just ahead of weather."