On core of $p$-prefrattini subgroup of a finite soluble group

Let $p$ be a prime, and $H$ is a $p$-prefrattini subgroup of a finite soluble group $G$. In the paper it is proved that there exist elements $x, y, z\in G$ such that the equality $H\cap H^x\cap H^y\cap H^z=\Phi_p(G)$ holds.