I assume you mean MapInfo SpatialWare, which is a supported format, so are various ESRI database flavors. So the short answer is: yes, this is possible. Depending on which specific ESRI database format you want to write to you may need at least an FME ESRI edition and ArcGIS licensed on the same computer, in other cases an FME Professional edition could be enough.

The steps you need to take can be as simple as using the FME Quick Translator, selecting your input database and your output database and hitting run. A next step up would be generating a workspace in the FME Workbench. This would be better if you want to repeat the process on a regular basis or make changes to the data during the process.

If you want to make a quick start, I'd recommend going through chapter 1 of the FME 2017 Desktop Basic Training Course.

If you have more specific questions about the data transformation process feel free to ask here.