Homomorphic Image of R-Module is R-Module

Theorem
Let $\left({G, +_G, \circ}\right)_R$ be an $R$-module.

Let $\left({H, +_H, \circ}\right)_R$ be an $R$-algebraic structure.

Let $\phi: G \to H$ be a homomorphism.

Then the homomorphic image of $\phi$ is an $R$-module.