Remark 2

Let (I, i) be an injective envelope of M. Identify M with the submodule $i(M)$ of I. For every submodule N of M, there exists an injective submodule of I which is an injective envelope of N (apply Remark 1 to N). Conversely, every injective submodule J of I is an injective envelope of $J \cap M$.