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Once you move your site to another directory you will have to manual edit the:
mainfile.php
Make sure you set the permisson to 777 for editing and set back to 444 after you finished.
Also the database,
If you want to use the same database for multiple site like for the same setting together and users, leave it.
If you want it to be different,
You might have to download the SQl files and edit each prefix to a unique name.
OR
you will have to make another database with another name and download and import or run the SQL query to make the data into the new database you just created and then you have to edit the mainfile.php to change the location or the database name (path)