macbook pro

I have recently successfully transferred data from my IPhone 6s to my new IPhone 13 mini, EXCEPT for the music library in its entirety.

I have used ITunes on the MacBook Pro (IOS El Capitán, 10.11.6, will update no further) to do this in the past.

The question: is there a way to transfer my music library from my MacBook Pro to the new phone? I have full backups of the MacBook Pro on my Time Machine.