Switching from Individual to Apple Music Family Account
When you switch to the Family Plan, can the person you invite keep their existing music if they accept your invitation?
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Yes. But do not cancel the individual subscription first. As it says in:
Get an Apple Music family subscription - Apple Support
"If someone in the family group already has an individual or student subscription to Apple Music, renewal of that subscription is automatically canceled when they join the family group." And they will retain their music library.