Can FME Desktop convert OSM map files to MapInfo MWS Workspace files?

FME doesn't have a native MapInfo MWS Workspace file writer. However, the MWS files are XML files and it seems the XSD's are freely available from Mapinfo in the Spectrum Spatial Guide. So you might be able to use the FME XML Templater and XML writer to create the MWS workspaces.

You might want to consider adding this as a New Idea to see if other FME users would vote to add this functionality into FME