In the present paper, we investigated the gravitational black-hole-hedgehog's solution with magnetic field contribution in the framework of the f(R)-gravity described by the Gravi-Weak unification model. Assuming the Multiple Point Principle (MPP), we considered the existence of the two degenerate vacua of the Universe: the first Electroweak (EW) vacuum with v 1 ≈ 246 GeV ("true vacuum"), and the second Planck scale ("false vacuum") with v 2 ∼ 10 18 GeV. In these vacua, we investigated different topological defects. The main aim of this paper is an investigation of the black-hole-hedgehog configurations as defects of the "false vacuum". We have obtained the solution which corresponds to a global monopole, that has been "swallowed" by the black-hole with core mass M BH ≈ 3.65 × 10 18 GeV and radius δ ≈ 6 · 10 −21 GeV −1 . We investigated the metric in the vicinity of the black-holehedgehog and estimated its horizon radius: r h ≈ 1.14δ. We have considered the phase transition from the "false vacuum" to the "true vacuum" and confirmed the stability of the EW-vacuum.