restriction of scalars of a module for a ringhomomorphism

Let \(R,S\) be rings, \(M\) an \(S\)-module and \(\varphi: R \rightarrow S\) Then \(M\) is an $R$-Module with

\begin{align*} r \cdot m \coloneqq& \varphi(r) \cdot m \end{align*}