You would have to download all the music files from Google Play first to your computer. Obviously, this cannot be done if your music is streaming only. You will need the physical files. After that, just add them to Groove/Media Player.
Google Music allows you 2 downloads... Unless you add some widget or other to open it up a bit. Stoopid really.
Whenever I have (rarely) made a purchase from G-Music, I immediately download it so I can do whatever I want with it. I mean, that's why I bought it, so I could have it.
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I guess I am old school, plus I don't have amazingly fast internet, but I prefer playing actual locally stored music, as opposed to streaming it all. Lots of streaming services either don't support my country or don't have what I want.