How to switch plan to Family Sharing

You will have to subscribe, invite her to your family plan, then have her leave her plan so she has continuous membership and doesn't lose her playlists, etc.

Click on this link to read how to 'Get an Apple Music Family subscription'--> https://support.apple.com/HT205595

To learn how to 'Set up Family Sharing', click here --> https://support.apple.com/HT201088

Yes, by doing it in that order. When she transitions from her account to yours she will have continuous membership.

The document I linked says:

"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."