B767 FO reported a track deviation occurred in their attempts to exit wake turbulence from the preceding A380 on their oceanic route.

Narrative

While at cruise; FL350; M.80; with SLOP offset; 1nm right of course (R1) and in smooth air (no turbulence) crew observed traffic on TCAS approximately 25nm ahead and 1000 ft. below (FL340); same track and what appeared to be the same 1R SLOP. Cruise winds at the time were showing a direct tailwind at approximately 70-80 kts. A few minutes later aircraft experienced a sudden onset of light to moderate turbulence -- while in an area where no turbulence conditions were forecast or expected. It was further observed by both crewmembers at the same time; that the preceding aircraft; still showing on TCAS (and on the same track and offset) was now climbing and had passed through FL350 and leveled at FL360. These conditions and timing indicated a jetwash/wake turbulence encounter from the preceding aircraft. Pilot Flying removed SLOP offset to '0' (or no offset) in an attempt to exit the wash/wake turbulence condition; however conditions persisted even after established on a zero offset course. Parallel to course tailwinds did not provide an 'upwind' offset. PF (Pilot Flying) and PM (Pilot Monitoring) elected to set R3 (non-standard) to exit the jetwash/wake turbulent condition while concurrently hailing preceding aircraft on Oceanic Interplane frequency. Upon reaching SLOP R3 offset; turbulence subsided. In addition; the preceding aircraft at FL360 was identified as an A380; and notified of the jetwash/wake they were providing. As a result of the communication with them; the A380 subsequently removed the R1 SLOP which eventually allowed us to return to SLOP R2 without further incident of wake/jetwash. Shortly after achieving an R3 offset and exiting the turbulence condition; Gander notified us twice via SELCAL to advise us that ATC was inquiring about the deviation. PM attempted to clarify R3 Offset condition was temporary for wake turbulence and not a deviation for navigation or weather. Once clarified and SLOP returned to R2; no further inquiries were made by ATC. Remainder of flight was uneventful.