We present and discuss the stellar kinematics and populations of the S0 galaxy FCC 170 (NGC 1381) in the Fornax cluster, using deep MUSE data from the Fornax 3D survey. We show the maps of the first four moments of the stellar line-of-sight velocity distribution and of the mass-weighted mean stellar age, metallicity, and [Mg/Fe] abundance ratio. The high-quality MUSE stellar kinematic measurements unveil the structure of this massive galaxy: a nuclear disk, a bar seen as a boxy bulge with a clear higher-velocity-dispersion X shape, a fast-rotating and flaring thin disk and a slower rotating thick disk. Whereas their overall old age makes it difficult to discuss differences in the formation epoch between these components, we find a clear-cut distinction between metal-rich and less [Mg/Fe]-enhanced populations in the thin-disk, boxy-bulge and nuclear disk, and more metal-poor and [Mg/Fe]-enhanced stars in the thick disk. Located in the densest region of the Fornax cluster, where signs of tidal stripping have been recently found, the evolution of FCC 170 might have been seriously affected by its environment. We discuss the possibility of its "preprocessing" in a subgroup before falling into the present-day cluster, which would have shaped this galaxy a long time ago. The thick disk displays a composite star formation history, as a significant fraction of younger stars co-exist with the main older thick-disk population. The former subpopulation is characterized by even lower-metallicity and higher-[Mg/Fe] values, suggesting that these stars formed later and faster in a less chemically evolved satellite, which was subsequently accreted. Finally, we discuss evidence that metal-rich and less [Mg/Fe]-enhanced stars were brought in the outer parts of the thick disk by the flaring of the thin disk.