Open the GIF in Messages, Safari, Photos, or another app
Tap and hold the GIF
Tap Save Image or Add to Photos
Open the Photos app
Find the GIF in Recents or Animated
If saving from Safari, tap the Share button first if needed
If the GIF is in an app that does not support saving, use Share and choose Save Image
If the GIF is sent through Messages, tap and hold the GIF, then tap Save
If the GIF does not animate in Photos, make sure it was saved as a GIF file and not converted to a still image