About one Galois embedding problem. II

For an odd prime $p$, the Galois embedding problem of an extension with elementary abelian $p$-group in an extension with the Galois group isomorphic to the group of unitriangular matrices over the finite field of order $p$ is considered. It is proved that the solvability of the maximal accompanying problem with central kernel of period $p$ is sufficient for the solvability of the original problem.