We have used deep MUSE observations to perform a stellar-kinematic and population analysis of FCC 153 and FCC 177, two edge-on S0 galaxies in the Fornax cluster. The geometrical definition of the different structural components of these two galaxies allows us to describe the nature of their thick disks. These are both old, relatively metal poor and [Mg/Fe]-enhanced, and their star formation history (SFH) reveals a minor younger component whose chemical properties suggest its later accretion. Moreover, the outer regions of these geometrically defined thick disks show higher values of metallicity and lower values of [Mg/Fe]. These stars probably formed in the thin-disk region and they were dynamically heated to form the flares present in these two galaxies. We propose different formation scenarios for the three populations of these thick disks: in-situ formation, accretion and disk heating. A clear distinction in age is found between the metal poor and [Mg/Fe]-enhanced thick disks (old, ∼12 − 13 Gyr), and the metal rich and less [Mg/Fe]-enhanced thin disks (young, ∼4 − 5 Gyr). These two galaxies show signs of relatively recent star formation in their thin disks and nuclear regions. While the thin disks show more continuous SFHs, the nuclei display a rather bursty SFH. These two galaxies are located outside of the densest region of the Fornax cluster where FCC 170 resides. This other edge-on S0 galaxy has recently been studied, and we have compared and discussed our results with this previous study. The differences between these three galaxies, at different distances from the cluster center, suggest that the environment can have a strong effect on the galaxy evolutionary path.