Normal automorphisms of a soluble product of abelian groups

Let $G$ be a soluble product of class $n\ge2$ of nontrivial free abelian groups. We prove that the subgroup of all automorphisms of $G$ identical on the last nonunit commutant $G^{(n)}$, coincides with the subgroup of all inner automorphisms corresponding to the elements of $G^{(n)}$. We also show that the subgroup of all normal automorphisms of $G$ coincides with the subgroup of all inner automorphisms.