= Solution
{c}
We prove $(ii)\Rightarrow(i)$. The central block <idempotents> split every finite-dimensional <module> into its block components. A nonzero <indecomposable representation>, in particular an indecomposable <projective module>, has only one such component; otherwise these give a nontrivial direct-sum decomposition.
Every <Jordan–Hölder factor> of a module in a block belongs to that block, since its central idempotent acts as identity on <submodules> and quotients. Thus any two simple factors of the same projective indecomposable are in the same block. Applying this along the proposed chain yields $\boxed{S,T\text{ belong to the same block}}$.
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