Moving app data to SD card help.

I have a Galaxy S4, I put some apps on my SD card and noticed that only part of the app went there. Some data stays on my internal storage. I went to my android folder in my internal storage and found 3 game folders there with a lot of memory, I figured I would move it to my SD card folder to save memory. However when I tried to play the game again it made me download it again, putting it right back in my internal storage. Is there no way to put all of the data on my SD card? I hope my question made sense. Thanks.

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