Let $A$ and $B$ be two cocomplete categories (i.e. closed under small colimits) and $A'$ be a dense subcategory of $A$ i.e. any object in $A$ is a colimit of objects in $A'$. Given a functor $F': A' \to B$, does there always exist an extension of functor $F :A \to B$ preserving all colimits?