  How do galaxies transform from blue, star-forming spirals to red, quiescent
early-type galaxies? To answer this question, we analyzed a set of 26 gas-rich,
shocked post-starburst galaxies with Hubble Space Telescope (HST) imaging in B,
I, and H bands, and Sloan Digital Sky Survey (SDSS) i-band imaging of similar
depth but lower resolution. We found that post-starbursts in our sample have
intermediate morphologies between disk- and bulge-dominated (S\'ersic
n$=1.7^{+0.3}_{-0.0}$) and have red bulges, likely due to dust obscuration in
the cores.
  Majority of galaxies in our sample are more morphologically disturbed than
regular galaxies (88%, corresponding to >3$\sigma$ significance) when observed
with HST, with asymmetry and S\'ersic residual flux fraction being the most
successful measures of disturbance. Most disturbances are undetected at the
lower resolution of SDSS imaging. Although ~27% galaxies are clear merger
remnants, we found that disturbances in another ~30% of the sample are
internal, caused by small-scale perturbations or dust substructures rather than
tidal features, and require high-resolution imaging to detect. We found a
2.8$\sigma$ evidence that asymmetry features fade on timescales ~200 Myr, and
may vanish entirely after ~750 Myr, so we do not rule out a possible merger
origin of all post-starbursts given that asymmetric features may have already
faded. This work highlights the importance of small-scale disturbances,
detected only in high-resolution imaging, in understanding structural evolution
of transitioning galaxies.
