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