It may help if you give a quick explanation (beyond just moving files) as to what you're trying to do. Apart from moving files, it looks like you're also trying to install something. It's a little confusing.
In order to use the file browser as root, you'd have to run:
That will allow you to use the file browser as root.
The error you're getting "...cannot stat common.txt..." is either a naming or permissions problem. To help clear it up, please run:
This will tell us if the file is really there and what permissions are set.
ls -l /home/test/Documents/
Finally, you don't need to switch user to root to do things. You can (and should) just use elevated privileges to run individual commands. So, let's assume that common.txt is in /home/test/Documents and you want to move it to /example (which by the way is different than ~/example...be careful!). Since / is owned by root (and depending on how you make /example, that directory may be as well), you'd run:
test@test-vm:/home/test/Documents# sudo mv common.txt /example/