I went to “free” Spotify so my lists still exist there. On amazon music (not Apple–I am an android-windows person and Amazon offered 3 months free plus one free audiobook/month) I made a query (or maybe I just googled) and found a free app that converted. It was much easier than I thought it would be.
I’ve done it, it’s a really good package. We opted for the upgraded Apple package that includes 2 Terabytes of iCloud. One thing to consider with Apple Music. It relies entirely on AirPlay. They don’t have the same kind of compatibility with smart speakers like Alexa, meaning that you can’t seamlessly play a song on the nearest Echo. You can still pair with Bluetooth or cast a song (Airplay) to a TV soundbar.
Is it free? When I moved my playlists from Spotify to Amazon Music, I googled to find a free app to do what you describe. It worked flawlessly. I don’t remember what I used, but googling “free playlist transfer” finds several apps that have free versions.
The answer is yes, but you can’t do it directly. There’s an app called “Tune My Music.” It acts as a go between to transfer playlists to Apple Music from Spotify. Otherwise he has to set them up manually and that’s a pain. My daughter opted to keep Spotify and pay for a $6 a month college plan to keep all her playlists intact.