Let $M$ be a representation of a quiver $Q=(V, E)$ by $R$-modules. By $M^{+}$ we mean a representation of $Q^{op}$ with $M^{+}(v)=\mathrm{Hom}(M(v), \frac{Q}{Z})$. One can easily see that there is anatural monomorphism $M\to M^{++}$ of representations of $Q$. Is it a pure monomorphism? That is, for any finitely presented representation $F$, can we prove that $ \mathrm{Hom}(F, M^{++})\rightarrow {\rm Hom}(F, \frac{M^{++}}{M})$ is an pimorphism?