grp\] Suppose $\phi: F \to F$ and $\psi:F' \to F'$ are free group injective endomorphisms such that $F *_\phi \cong F' *_\psi$. Then $\phi$ is induced by a pseudo-Anosov if and only if $\psi$ is induced by a pseudo-Anosov.  Without loss of generality, suppose $\phi$ is induced by a pseudo-Anosov 