Why won't my music move over to my phone?
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First thing I would check is to compare the song's purchase ID to your current Apple ID. Almost everyone has more than one AppleID in their lives so it's not uncommon to see songs from different AppleID's through the years. To find out this, select the song in the Music app and right click to "Get Info". Then select file. The next window will show what appleID purchased the song. If this is the same as your current AppleID on your phone, then the problem lies elsewhere. But there's where I'd start.