  Stellar kinematics provide insights into the masses and formation histories
of galaxies. At high redshifts, spatially resolving the stellar kinematics of
quiescent galaxies is challenging due to their compact sizes. Using deep
near-infrared spectroscopy, we have measured the resolved stellar kinematics of
four quiescent galaxies at z=1.95-2.64, introduced in Paper I, that are
gravitationally lensed by galaxy clusters. Analyses of two of these have
previously been reported individually by Newman et al. and Toft et al., and for
the latter we present new observations. All four galaxies show significant
rotation and can be classified as "fast rotators." In the three systems for
which the lensing constraints permit a reconstruction of the source, we find
that all are likely to be highly flattened (intrinsic ellipticities of
$\approx0.75-0.85$) disk-dominated galaxies with rapid rotation speeds of
$V_{\rm max}=290-352$ km/s and predominantly rotational support, as indicated
by the ratio $(V/\sigma)_{R_e}=1.7-2.3$. Compared to coeval star-forming
galaxies of similar mass, the quiescent galaxies have smaller $V/\sigma$. Given
their high masses $M_{\rm dyn} \gtrsim 2\times10^{11} M_{\odot}$, we argue that
these galaxies are likely to evolve into "slow rotator" elliptical galaxies
whose specific angular momentum is reduced by a factor of 5-10. This provides
strong evidence for merger-driven evolution of massive galaxies after
quenching. Consistent with indirect evidence from earlier morphological
studies, our small but unique sample suggests that the kinematic
transformations that produced round, dispersion-supported elliptical galaxies
were not generally coincident with quenching. Such galaxies probably emerged
later via mergers that increased their masses and sizes while also eroding
their rotational support.
