Epimorphism Preserves Modules

Theorem
Let $$G$$ be an $R$-module.

Let $$H$$ be an $R$-algebraic structure.

Let $$\phi: G \to H$$ be an epimorphism.

Then $$H$$ is an $R$-module.

It follows that the homomorphic image of an $R$-module is an $R$-module.

Corollary
If $$G$$ is a unitary $R$-module, then so is $$H$$.