If this was Windows I would just select, cut and paste. That is the normal way of moving files around.
A safer way is to select, copy and paste, and then test whether the file in the new location works properly. If so, then it is safe to delete the original.
I assume that is the same in Macs and Linux.
I have a number of audio books which are in my iTunes "songs" folder. How can I move them to my "Audio books" folder?