Implication details

Proof: Let $\C$ be a finitely accessible category and let $G$ be an essentially small collection of finitely presentable objects which generates $\C$ under filtered colimits. Consider $G$ as a full subcategory and consider the restricted Yoneda embedding $\C \hookrightarrow [G^{\op},\Set]$. It preserves filtered colimits (essentially by the definition of a finitely presentable object) and all limits, in particular monomorphisms. It also reflects monomorphisms since $G$ is a generating collection. Therefore, since $\Set$ and hence the functor category has filtered-colimit-stable monomorphisms, this is also true for $\C$.