= Solution
Let $S,T$ be <module sources> at $D$. Since $S\mid M\downarrow_D$ and $M\mid T\uparrow^G$, <Mackey decomposition> gives
$$
S\mid\operatorname{Res}_D^G\operatorname{Ind}_D^G T
\cong\bigoplus_{g\in D\backslash G/D}
\operatorname{Ind}_{D\cap{}^gD}^D
\operatorname{Res}_{D\cap{}^gD}^{{}^gD}({}^gT).
$$
The <module source> $S$ has <module vertex> $D$. By <Krull–Schmidt theorem> it is a summand of one term, and minimality of its <module vertex> forces $D\cap{}^gD=D$. As both <subgroups> have order $|D|$, $g\in N_G(D)$. The corresponding term is simply ${}^gT$, which is indecomposable. Thus
$$
\boxed{S\cong{}^gT\quad\text{for some }g\in N_G(D).}
$$
This proves conjugacy of <sources of an indecomposable module> at the specified <module vertex>.
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