From previous expierence, you should just be able to move the files with no problems and still have it work. The only potential roadblock I can think of is that there maybe some absolute paths for keys like `home` who’s values don’t update automaticly (in the `wp_options` table) so you might need to update their values manually so you may need to jump in make sure they’re pointing to the right locations. This change may also need to be made for any assets you link up on the site that also use absolute paths.
Be aware also that you will need to move the `.htaccess` file from the old root to the sub directory (otherwise your URL re-writting among other things will break). If you are using a GUI to move files, this is often not shown by default. Therefore, you will need to enable showing hidden files to verify that it gets moved as well.