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We investigate the hadron-quark phase transition at nite density in the presence of a magnetic eld taking into account the anisotropy created by a uniform magnetic eld in the system's equations of state.We fi nd a new anisotropic equilibrium condition that will drive the fi rst-order phase transition along the boundary between the two phases. Fixing the magnetic eld in the hadronic phase, the phase transition is realized by increasing the baryonic chemical potential at zero-temperature. It is shown that the magnetic eld is mildly boosted after the system transitions from the hadronic to the quark phase. The magnetic- eld discontinuity between the two phases is supported by a surface density of magnetic monopoles, which accumulate at the boundary separating the two phases. The mechanism responsible for the monopole charge density generation is discussed. Each phase is found to be paramagnetic with higher magnetic susceptibility in the quark phase. The connection with the physics of neutron stars is highlighted throughout the paper.