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Formation and evolution of dwarf early-type galaxies (dE/dS0), which constitute the majority of galaxy populations in clusters still remains a matter of debate. It is also unclear whether they share common origin with much more extended ultra-diffuse galaxies (UDGs). We identified 13 low-mass post-starburst galaxies (PSGs) using RCSED (http://rcsed.sai.msu.ru/), 11 of which reside in the Coma cluster and 4 of 11 show clear signs of recent ram pressure stripping as comet-like tails. Given the lack of current star formation, we can call them post-jellyfish galaxies. We followed up 11 of them with the new high-throughput multi-object spectrograph Binospec at the MMT. Using spectrophotometric fitting with dedicated stellar population models we reconstructed their star-formation and metal-enrichment histories. Our analysis suggests that 10 galaxies will evolve into UDGs in the next 5 Gyr and one will become a dE. As filler targets for the multi-object spectroscopy we chose UDGs from the Yagi+15 catalog. We determined spatially resolved velocity profiles and integrated velocity dispersions and stellar population properties for 9 galaxies, 2 of which have intermediate ages and overall properties between UDGs and low-mass post-jellyfish galaxies. These results confirm the direct evolutionary link between diffuse post-starburst galaxies and UDGs and prove that ram pressure stripping as one of the channels of UDG and dE/dS0 formation in clusters.