  Recent studies have suggested that type Iax supernovae (SNe Iax) are likely
to result from a weak deflagration explosion of a Chandrasekhar-mass white
dwarf in a binary system with a helium (He)-star companion. Assuming that most
SNe Iax are produced from this scenario, in this work we extend our previous
work on the three-dimensional hydrodynamical simulation of ejecta-companion
interaction by taking the orbital and spin velocities of the progenitor system
into account. We then follow the post-impact evolution of a surviving He-star
companion by using the one-dimensional stellar evolution code \textsc{MESA}. We
aim to investigate the post-explosion rotation properties of a He-star
companion in SNe Iax. We find that the He-star companion spins down after the
impact due to the angular-momentum loss and expansion caused by the
mass-stripping and shock heating during the interaction. This leads to the
situation where the surface rotational speed of the surviving companion can
drop to one-third of its pre-explosion value when it expands to a maximum
radius a few years after the impact. Subsequently, the star shrinks and spins
up again once the deposited energy is released. This spin-switching feature of
the surviving He-star companions of SNe Iax may be useful for the
identification of such objects in future observations.
