Q: How to authorize a computer if the previous apple ID is no longer active?

You can't transfer music from one Apple ID to another.  Family Sharing can provide a workaround but even that has limitations and requires an Apple ID.

Not really. You have to authorize your new computer with your iTunes Store account. You can use library, Home or Family Sharing to access what is in her library.

Set up Family Sharing - Apple Support

But you need to recover the Apple ID before starting this as it requires the Apple ID to work. 

If you forgot your Apple ID password - Apple Support