So yeah, just open your MB and then use its file organizer to move your files to your new SSD.
By doing so, you get to keep your play counts and data like that (as explained on the MB wiki page I linked you to).
Concerning the location of your MB program, I only asked that to confirm whether or not it was on the failing "H" drive.
But now that you've cleared that up, there's no follow up on that regard.