How to move existing files from public to private folder

I am looking for an easy and secure way to move a bunch of existing files from public to private folder.

I could do it "manually" but it seams FFP could be of great help while I cannot find any clear tutorial.
I only need to move the files. Same structure. Same file names. I only want to change uri from piblic://blablabla to private://blablabla
Please, how to proceed?
- Can FFP do all the work for me? (I mean updating database and physically move the files to the private folder)
- Should I move the files manually and then FFP will update de data base?

Of course I could test in a sandbox site but if some one could clarify this process I woul appreciate (and save time!)

Thanks in advance.