Suppose $0\to F\to G \to H\to 0$ is an exact sequence of group schemes (over some base scheme $S$) by which I mean that the corresponding sequence of fppf-sheaves is exact.
I read somewhere that the surjectivity of the sequence of fppf-sheaves is equivalent to the fact that the morphism $G\to H$ is fppf (faithfully flat and locally of finite presentation).
I was able to prove one of the directions: If $G\to H$ is fppf then the sequence of fppf-sheaves is surjective.
I'm not sure how to prove the other direction. Any help/reference would be much appreciated.