= Solution
Choose bases $S_1=\mathbb Cs_1$, $S_2=\mathbb Cs_2$ and set
$$
\begin{pmatrix}r&s\\0&t\end{pmatrix}s_1=rs_1,
\qquad
\begin{pmatrix}r&s\\0&t\end{pmatrix}s_2=ts_2.
$$
Both are <simple modules>. They are nonisomorphic because $e_{11}$ acts as the identity on $S_1$ and as zero on $S_2$. In the ascending <composition series of a module> above, the factors are, in order,
$$
\boxed{S_1,\ S_1,\ S_2.}
$$
The last factor is represented by $e_{22}$ modulo the span of $e_{11},e_{12}$.
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