GIF Viewer Extra

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Back-up and device sharing of app data enabled. Which will help transfer all of your files included in this app to another device.
If that doesn't work or if you only want to move one folder out of this app, you can use the new Export option. This makes a copy of selected folders (and files + sub-folders) availbable to other apps, like File Explorer. With that latter app you can move the data out of GifViewer to shared Android storage (like DCIM folder). See the website for details.