  In this note, we show that a ring $R$ is $S$-coherent if and only if every
finitely presented $R$-module is $S$-coherent, providing a positive answer to a
question proposed in [D. Bennis, M. El Hajoui, {\it On $S$-coherence}, J.
Korean Math. Soc. \textbf{55} (2018), no.6, 1499-1512]. Besides, we show that
$c$-$S$-coherent rings are $S$-coherent, and give an example to show the
converse is not true in general.
