Part of the third Isomorphism theorem for modules
As answered in the comments, If $I$ is a submodule of $\frac{M}{T}$, the submodule of M given by $S = \{ m \in M : m + T \in I \} $ gives $ T \subseteq S \subseteq M$ and $I = \frac{S}{T} $.
As answered in the comments, If $I$ is a submodule of $\frac{M}{T}$, the submodule of M given by $S = \{ m \in M : m + T \in I \} $ gives $ T \subseteq S \subseteq M$ and $I = \frac{S}{T} $.