Widebody; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Time Pressure; Training / Qualification
Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Requested ATC Assistance / Clarification
Human Factors; Procedure
I was the flying pilot. The Captain was on break. The FO was the NFP. We were level at FL370. The oceanic clearance stated SUPRY/XA43 MNTN F390 M83. I took that to mean we were to cross SUPRY at 390 and initiated a climb approaching the fix. The Gander Controller questioned our altitude and said we should have ask for climb clearance. He said we could remain at 390. There was no conflicts with other aircraft and initially there was no problem. Later we were informed by the controller he would have to file a report.
When I returned from my break I was informed that the Oceanic clearance was received and part of the clearance was to maintain fl390 and .83 Mach. The FB was the pilot flying in the left seat and FO was the Pilot monitoring. The FO assumed he was cleared to climb to 390 by SUPRY. Approaching the entry point SUPRY he initiated the climb. Gander told him he climbed without clearance. Initially the controller didn't think it was a problem but his supervisor said they needed to report it because it has been a reoccurring problem.
A widebody transport flight crew received their oceanic track clearance which included a cruising level of FL390.  They were level at FL370.  The Flying Pilot climbed to FL390 without clearance from Gander Center.