Conjugacy subgroups in nilpotent groups

The main result of the present note is following
Theorem 2.I . Let $G$ be a finitely-generated nilpotent group and let $A$, $B$ be subgroups of $G$ which are not conjugate in $G$. Then there is an epimorphism $\varphi$ of $G$ onto a finite group $H$ such that $A\varphi$ and $B\varphi$ are not conjugate in $H$.