Let $G$ be a finite abelian group and $H$ be a subgroup of $G$. Then there is an epimorphism from $G$ to $H$. Let $G$ be a finite abelian group and $H$ be a subgroup of $G$. Then there is an epimorphism from $G$ to $H$.
(That is, an epimorphism from a finite abelian group to its subgroup.)

It follows from the structure theorem of finitely generated abelian groups that a finite abelian group $G$ is (not canonically) isomorphic to its character group $\def\ch#1{\operatorname{Hom}(#1,\mathbb{Q}/\mathbb{Z})}\ch{G}$. Moreover, the functor $\ch{{-}}$ maps epimorphisms into monomorphisms and conversely.
So if you have $H$ a subgroup of $G$, consider the epimorphism $\ch{G}\to\ch{H}$ obtained from the inclusion and use the isomorphisms $G\cong\ch{G}$ and $H\cong\ch{H}$.
