  Motivated by measurements of the rotation speed of accretor stars in
post-mass-transfer (post-MT) systems, we investigate how magnetic braking
affects the spin-down of individual stars during binary evolution with the
MESAbinary module. Unlike the conventional assumption of tidal synchronization
coupled with magnetic braking in binaries, we first calculate whether tides are
strong enough to synchronize the orbit. Subsequently, this influences the
spin-down of stars and the orbital separation. In this study, we apply four
magnetic braking prescriptions to reduce the spin angular momentum of the two
stars throughout the entire binary evolution simulation. Our findings reveal
that despite magnetic braking causing continuous spin-down of the accretor,
when the donor begins to transfer material onto the accretor, the accretor can
rapidly spin up to its critical rotation rate. After MT, magnetic braking
becomes more important in affecting the angular momentum evolution of the
stars. Post-MT accretor stars thus serve as a valuable testbed for observing
how the magnetic braking prescriptions operate in spinning down stars from
their critical rotation, including the saturation regimes of the magnetic
braking. The rotation rate of the accretor star, combined with its mass, could
provide age information since the cessation of MT. By comparing the models
against observation, the magnetic braking prescription by Garraffo et al.
(2018b) is found to better align with the rotation data of post-MT accretors.
