From ##(5)## we have
\begin{align*}
ed\equiv 1 \mod \phi(n) &\Longleftrightarrow \phi(n)\,|\,(ed-1) \\
&\Longleftrightarrow \phi(n)\cdot k = ed-1 \text{ for some } k \in \mathbb{Z}\\
&\Longleftrightarrow \phi(n)\cdot k +1 = ed \text{ for some } k \in \mathbb{Z}\\
&\Longrightarrow M^{\phi(n)\cdot k +1} =M^{ed}
\end{align*}