  This paper focuses on a question raised by Holm and J{\o}rgensen, who asked
if the induced cotorsion pairs $(\Phi({\sf X}),\Phi({\sf X})^{\perp})$ and
$(^{\perp}\Psi({\sf Y}),\Psi({\sf Y}))$ in $\mathrm{Rep}{Q}{\sf{A}}$--the
category of all $\sf{A}$-valued representations of a quiver $Q$--are complete
whenever $(\sf X,\sf Y)$ is a complete cotorsion pair in an abelian category
$\sf{A}$ satisfying some mild conditions. Recently, Odaba\c{s}{\i} gave an
affirmative answer if the quiver $Q$ is rooted and the cotorsion pair $(\sf
X,\sf Y)$ is further hereditary. In this paper, we significantly improve
Odaba\c{s}{\i}'s work by establishing the same result in the much more general
framework of functor categories, and at the same time removing the hereditary
assumption on the cotorsion pair.
