A module $M$ is called H-supplemented if for every submodule $N$ of $M$ there exists a direct summand $D$ of $M$ such that $M = N + X$ if and only if $M = D + X$ for every submodule $X$ of $M$.
A module $M$ has $D2$ if $A\leq M$ such that $M/A$ is isomorphic to a direct summand of $M$, then $A$ is a
direct summand of $M$.
The question is: Does H-supplemented imply D2?