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Quality of stellar mass determination for galaxies, which contain a mix of old and young stellar populations crucially depends on detailed star formation histories. Using Reference Catalogue of Spectral Energy Distribution of galaxies (RCSED), we have recently identified a sample of 13 low-mass diffuse (half-light radii of 2 to 4 kpc) post-starburst galaxies with very young mean stellar ages in two galaxy clusters and then obtained deep follow-up spectroscopic observations for 11 of them using the Binospec spectrograph at the 6.5-m MMT. The three main questions we are trying to answer are: (i) how did they form; (ii) how much dark matter do they contain; (iii) what will happen to them in future. We used the NBursts+phot code to extract parametrized star formation histories (SFHs) from spectra and broadband photometric data simultaneously. Starting from a set of pre-computed simple stellar populations (SSPs), we constructed a grid of stellar population models aimed at reproducing the simplest but realistic evolutionary scenario for these galaxies in the cluster environment affected by ram pressure. Every model is a combination of a truncated constant SFH with a self-consistent metallicity evolution computed in the framework of the instant recycling approximation, that represents an evolution of a low-mass galaxy prior to the moment it entered the cluster; and an SSP at the end of the SFH, which represents the starburst induced by the ram pressure prior to the total stripping of gas and star formation cessation. By fitting observational data against these models for every galaxy we estimated: (i) the average star formation rate in the constant SFR phase and the total stellar mass formed (1--3*108 MSun); (ii) the star formation quenching epoch (300-500Myr); (ii) the total mass formed during the final starburst event prior to quenching (30-50% of the total M*). These models provide statistically better quality of fitting of our data compared to SSPs. They also result in higher stellar M/L ratios by a factor of 1.5--2 than SSPs, which suggests the dark matter fraction of 50--70% within the 2 effective radii based on the results of our dynamical modeling. Finally, our analysis suggests that in 3-5 Gyr these galaxies will fade down in surface brightness and transform into ultra-diffuse galaxies, whose formation and evolution is currently not well understood. Hence, in our study we demonstrate that currently available spectroscopic data have sufficient quality for extraction of realistic parametric SFHs for simple low-luminosity galaxies; and that ram pressure induced star formation and consequent stripping can explain the formation of ubiquitous ultra-diffuse galaxies in clusters and, hence, solve one of the actively discussed questions of galaxy evolution.