The congruence-kernel identification for free metabelian groups

Let $\Phi_r$ be the free metabelian group on two generators, and let $\Phi_{r,n}$ denote the corresponding finite quotient modulo the relevant power-$n$ congruence subgroup. Using the isomorphism $Out(\Phi_r)\cong GL_{2}(\mathbb{Z})$, consider the induced maps to $Out(\Phi_{r,n})$ and to $GL_{2}(\mathbb{Z}_{n^r})$. Congruence-kernel conjecture. For $r,n\in\mathbb{N}$,

$$\ker\bigl(Out(\Phi_r)\to Out(\Phi_{r,n})\bigr)=\ker\bigl(GL_{2}(\mathbb{Z})\to GL_{2}(\mathbb{Z}_{n^r})\bigr).$$

This identifies the kernel of the outer automorphism action on the finite quotient with the corresponding principal congruence kernel under $Out(\Phi_r)\cong GL_{2}(\mathbb{Z})$. The supplied text does not state whether the claim has been proved or remains open.