Unfortunately, it is not currently possible to publish animated GIFs to Facebook and Instagram hrough any third party tool such as MavSocial
However, it is possible to use a video version of your GIF. You can create your own MP4 files if you have the resources to do so and then upload the short video within MavSocial.
If you have a GIF file, you can also upload it to a free tool such as Giphy, and then download it in MP4 format. This video file (MP4) can then be uploaded into MavSocial