The person that falls is not Moriarty’s dead body. It is clear that the person falling is both (a) Sherlock and (b) moving (which rules out the cunning mask hypothesis)
As Watson runs around the corner (and gets knocked over (deliberately) to stop him getting too close) we see a lorry with a green and white cover on it. This lorry has a crash mat on it which Sherlock jumps onto. He then jumps from this onto the pavement and uses a blood bag (possibly provided by Molly) to make his injury seem bad. He is taken into the hospital and Molly arranges a replacement body which is buried.
It is notable that Sherlock commands Watson to “go back” and “stay where he is” which means that Watson is behind a lower building that conceals the actual point of impact.
It is also noteworthy that Moriarty talks about Sherlock heading for a fall, but that Sherlock chooses the venue for the denoument as being as specific high place, which gives him the opportunity to arrange the lorry with the crash mat in anticipation of this.
I am not sure, however, that Moriarty is dead.