  We show that superconducting correlations in the presence of non-zero
condensate velocity can mediate the peculiar interaction between localized
spins that breaks the global inversion symmetry of magnetic moments. The
proposed interaction mechanism is capable of removing fundamental degeneracies
between topologically distinct magnetic textures. For the generic system of
three magnetic impurities in the current-carrying superconductor we find the
energy term proportional to spin chirality. In realistic
superconductor/ferromagnetic/superconductor setups we reveal significant energy
differences between various magnetic textures with opposite chiralities. We
calculate Josephson energies of junctions through left and right-handed
magnetic helices as well as through the magnetic skyrmions with opposite
topological charges. Relative energy shifts between otherwise degenerate
magnetic textures in these setups are regulated by the externally controlled
Josephson phase difference. The suggested low-dissipative manipulation with the
skyrmion position in a racetrack geometry can be used for the advanced
spintronics applications.
