Apple Device

Depending on your software version, the process to save to your phone may look a little different. Sometimes you can long hold on the GIF in the folder, and save to your device. Sometimes you have to look for the settings button, and save that way. Try a few things out, but at the end what you want is for the gif to be saved into your regular picture gallery.

Android Device

If you have an Android, Save GIFs to your device, Download Giphy app from play store, upload GIFs to Giphy app. Then you can select a GIF and it will copy it. From there you can paste into IG story.