  One of the challenges in understanding the quenching processes for galaxies
is connecting progenitor star-forming populations to their descendant quiescent
populations over cosmic time. Here we attempt a novel approach to this
challenge by assuming that the underlying stellar mass distribution of galaxies
is not significantly altered during environmental quenching processes that
solely affect the gas content of cluster galaxies, such as strangulation and
ram-pressure stripping. Using the deep, high-resolution photometry of the
Hubble Frontier Fields, we create resolved stellar mass maps for both cluster
and field galaxies, from which we determine 2D S\'ersic profiles, and obtain
S\'ersic indices and half-mass radii. We classify the quiescent cluster
galaxies into disk-like and bulge-like populations based on their S\'ersic
indices, and find that bulge-like quiescent galaxies dominate the quiescent
population at higher masses ($M_\star > 10^{9.5}M_\odot$), whereas disk-like
quiescent galaxies dominate at lower masses ($10^{8.5}M_\odot< M_\star <
10^{9.5}M_\odot$). Using both the S\'ersic indices and half-mass radii, we
identify a population of quiescent galaxies in clusters that are "morphological
analogues" of field star-forming galaxies. These analogues are interpreted to
be star-forming galaxies that had been environmentally quenched. We use these
morphological analogues to compute the environmental-quenching efficiency, and
we find that the efficiency decreases with increasing stellar mass. This
demonstrates that environmental quenching is more effective on less massive
galaxies and that the effect of environment on quenching galaxies is not
completely separable from the effect of mass on quenching galaxies.
