Maximal normal subgroups of the automorphism groups of free nilpotent groups

We prove that the subgroup of all IA-automorphisms of the automorphism group $\operatorname{Aut}N$ of a free nilpotent group $N$ of infinite rank is normality-small. As a consequence, every maximal normal subgroup of the group $\operatorname{Aut}N$ is a lifting of a maximal normal subgroup of the automorphism group $\operatorname{Aut}A$ of the abelianization $A=N/[N,N]$ of $N$.