Well there’s a couple of things to think about here.
In WordPress there will be a export button somewhere. You can export this info (as an XML) and then on a clean install on your sub directory upload that XML.
If you move the site by FTP, it’ll be a bit more complicated. You then have to deal with uploading a mysql database, backups, etc.
The best part about the xml method is that you can actually skip changing .htaccess and other permalink stuff because you do a clean install on subdirectory first.