Sequential rectifiable spaces of countable $cs^*$-character

We prove that each non-metrizable sequential rectifiable space $X$ of countable $cs^*$-character contains a clopen rectifiable submetrizable $k_\omega$-subspace $H$ and admits an open disjoint cover by subspaces homeomorphic to clopen subspaces of $H$. This implies that each sequential rectifiable space with countable $cs^*$-character either is metrizable or else is a topological sum of submetrizable $k_\omega$-spaces. Consequently, $X$ is submetrizable and paracompact. This answers a question of Lin and Shen posed in 2011.