  Recently new topological phase of superfluid $^3$He has been discovered --
the $\beta$ phase, which is obtained by strong polarization of the nematic
polar phase. We consider half-quantum vortices, which are formed in rotating
cryostat, and discuss the evolution of the vortex lattice in the process of the
transition from the polar phase to the $\beta$-phase via the spin-polarized
polar phase.
