  I apply the recently developed formalism of generalized quasiclassical theory
to show that using hybrid superconducting systems with non-collinear strong
ferromagnets one can realize the Josephson junction between Berezinskii-type
superconductors. The reported calculation reproduces main features observed in
the recent experiment, namely the the slightly asymmetric double-slit
Fraunhofer interference pattern of the Josephson current through the
ferromagnetic vortex. The double-slit structure results from the spatially
inhomogeneous Berezinskii state with the amplitude controlled by the local
angle between magnetic moments in two ferromagnetic layers. The critical
current asymmetry by the sign of magnetic field can signal the presence of
spontaneous supercurrents generated by the non-coplanar magnetic texture near
the core of the ferromagnetic vortex core. I demonstrate that ferromagnetic
vortex can induce spontaneous vorticity in the odd-frequency order parameter
manifesting the possibility of the emergent magnetic field to create
topological defects.
