Aluffi: submodule $\Longleftrightarrow$ cokernel?

Question

Aluffi makes the following brief statement, in the context of modules: "The last sentence of Proposition 6.2 simply reiterates the slogan

submodule $\Longleftrightarrow$ kernel

and its mirror statement (which is just as true). Further details are left to the reader."

By the mirror statement, does he mean that if $N' \subset N$ is a submodule, then there exists a module $M$ and an $R$-module homomorphism $\varphi \colon M \to N$ such that $N' \cong N / \text{Im}(\varphi)$? If this is what he means, then I am having trouble proving it.

I'm wondering if I'm missing something obvious.

Thanks.

Answer 1

The answer in the comments sufficed for me.