Section view only affects the model visually inside Shapr3D, it won’t be present in any format other than .shapr.
For this use case, I would create a construction plane, place it where you want the section view to be, cut the design with split body tool using the construction plane, then hide half or the design which you don’t want to export. After that, you only need to export the visible part, and import it to Morpholio.
Make sure to select Keep originals in Split body tool if you also want to keep an unsplit version, or duplicate the whole design on the Designs page so you have the full version too.