How to transfer ripped music CDs from an old iMac to a new MacBook

I have a lot of ripped music cd’s on a rather old iMac. I copy the music to my iPhone & that all works really well.

I just went to buy a new MacBook. Sadly I was told by the Apple assistant in the store that my ripped music won’t work when transferred to the new MacBook. Apparently it’s something to do with licensing but I bought and paid for all that music!

Is there a solution please?

[Re-Titled By Moderator]