I know I am late to the conversation but I found a fix...atleast for me. In the settings menu in the Google Play Music app you can choose where your downloads are stored. CHOOSE external sd card. Once you downloaded your song navigate to your preferred file storage app, I use ES File Explorer. Go to your External SD card..then Android..then data...then..com.google.android.music...then files...then music. Your downloaded music will be listed as numbers.mp3 For example: 1236.mp3....from there you can rename/move the file to where you would like.