Depends what subfolders and the manner of your move as well as if the artwork was actually embedded in the files. If embedded, they would have come across with the files. If not there is a folder in iTunes folders with the artwork I think.
I guess I have successfully solved that. Somehow predicted this problem's appearance and added a function of ID3 tags version conversion. Just convert all of your mp3 files' tags to version 2.4. worked for me, now bitrate gets downgraded and artwork is safe.
p.s.: some of the artwork (especially files that originally were higher bitrate AAC converted to 128 kbit/s) won't show the artwork in the artist or album list at first. just play any of such songs and artwork will show up.