For future reference... a GIF is an image. So no need to call them something else.
So, first, try restarting (turning off and back on) the phone. That may well resolve your problem.
If that doesn't help, then you need to go into your browser's settings and see where it is set to save the images. It may not be somewhere that the gallery looks. If it does list where, then I would suggest changing the location to somewhere you prefer.
If you can't find it that way, then I would suggest finding another image to test with. When you go to save it, make sure you note the name of the file. Then use your phone's "File Manager" app (if it doesn't have one you can get one) and search the files for that name. You can also connect the phone to a computer, via USB cord, and search the phone from the computer.