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First a warning, run as root only what can't be run as a normal user. This
is especially true for X clients because of the way X clients can interact
with each other.
Now for your particular issue. You need to get the MIT-MAGIC-COOKIE-1 value
from the normal remote user with access to the X server and add it to the
root's authorization file (.Xauthority).
First to get the MIT-MAGIC-COOKIE-1 value from the normal remote user. Open
a ssh to the normal user account and run the following command.
xauth extract - $DISPLAY > /tmp/xauth.bin
This command will write the X authorization information for the current X
display to /tmp/xauth.bin
Now, open a terminal for the root (probably using the command "su -") and
run the following command.
xauth -v merge - < /tmp/xauth.bin
You should see output similar to the following.
# xauth -v merge - < /tmp/xauth.bin
Using authority file /home/artur/.Xauthority
1 entries read in: 0 new, 1 replacement
Writing authority file /home/artur/.Xauthority
Now try running a X client (e.g. xclock).
Regards.
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