With the "Fall of the Roman Empire" people most of the time refer to the fall of the Western part. The common date for that is 476, although many would say it was earlier or later. That would be around 100 before the estimated birth of Prophet Mohammed. So the answer would be "none".

If you are refering to the fall of the Eastern part, "Byzantine", in 1453 then that's a whole different subject that allows many lines to be drawn, but I doubt you could find any historian that would say Mohammed ( the historic person, seeing past any religious perspective) himself led to it. It was actions built upon actions for almost 900 years.