Right at the beginning of "Back To The Future" - part 3, after the night Marty brought the fainted Doc home, in the morning Marty woke up resting his feet on the hover board. Now, how did the hover board get there? .. The night before, when the letter from the 1885 Doc was handed to Marty by the Western Union guy, he ran away from that place to the "only man who can help him" - the 1955 Doc and her ran away obviously without taking the hover board, but letting it stay near the bucket where he burned the almanac. Also, when reaching the place where the 1955 Doc fainted, it can be seen clearly that he was not carrying the hover board.