On intersection of two nilpotent subgroups in finite group with socle $\Omega_8^+(2)$, $E_6(2)$ or $E_7(2)$

Let $G$ be a finite group with the socle $\Omega_8^+(2)$, $E_6(2)$ or $E_7(2)$. In this paper, it is given a description of all pairs $(A, B)$ of nilpotent subgroups $A$ and $B$ of $G$ such that $A\bigcap B^g\ne1$ for any $g\in G$.