  Galaxies infalling into clusters undergo both star-formation quenching and
morphological transformation due to environmental effects. We investigate these
processes and their timescales using a local sample of 20,191 cluster and
11,674 field galaxies from SDSS. By analysing morphology as a function of
distance from the star-formation main sequence, we show that environmental
influence is especially pronounced for low-mass galaxies, which emerge from the
green valley with early-type morphologies before their star formation is fully
suppressed. Using the galaxies' positions in the clusters' Projected Phase
Space, we examine the evolution of blue cloud, green valley, and red sequence
fractions as a function of time since infall. Interestingly, the green valley
fraction remains constant with time since infall, suggesting a balanced flow of
galaxies in and out of this class. We estimate that galaxies less massive than
$10^{10}\rm M_{\odot}$ spend approximately 0.4 Gyr in the green valley. By
comparing quenched and early-type populations, we provide further evidence for
the ``slow-then-rapid'' quenching model and suggest that it can also be applied
to morphological transitions. Our results indicate that morphological
transformation occurs at larger radii than complete star-formation quenching.
About 75% of galaxies undergoing morphological transition in clusters are
spirals evolving into S0s, suggesting that infalling galaxies retain their
disks, while massive ellipticals are relics of early merger events. Finally, we
show it takes approximately 2.5 and 1.2 Gyr after the delay-time ($\sim 3.8
{\rm Gyr}$) for the population of low mass galaxies in clusters to reach a 50%
threshold in quenched and early-type fraction, respectively. These findings
suggest morphological transition precedes full star formation quenching, with
both processes possibly being causally linked.
