I should note that, rather than write the move that gives checkmate (QxB), he simply wrote "checkmate" on his sheet. LOL.
Game 3, part 1.
At this point, he and his opponent didn't realize that you cannot castle through check so I needed to set up the board on this as part 2:
Game 4. His notation got confusing so I stopped the post where it stopped making sense. I'm He did win the game. I'll update if I can figure out what moves he forgot to write down.
The notation stopped here. Probably ended with the back rank mate, but it isn't locked in on his notation.