sudo emacsclient can't find the path to the user emacsserver.

[Clément Aymé]

Here is the case:
I got a emacsserver running as a Linux ubuntu normal user that is 
working fine.
When I switch under sudo the path to the emacsserver is lost:

For example
sudo emacsclient /etc/udev/rules.d/51-android.rules
returns
emacsclient: can't find socket; have you started the server?
To start the server in Emacs, type "M-x server-start".
emacsclient: No socket or alternate editor. Please use:

--socket-name
--server-file (or environment variable EMACS_SERVER_FILE)
--alternate-editor (or environment variable ALTERNATE_EDITOR)

And what I would like is to use the same emacs server as in user mode 
not having any additional one ...

Also this doesn't work as it is said into the sudo manual
sudo -u <username> emacsclient ....
the file is effectively loaded into the emacs server but still remains 
read-only
so any help welcome...

What could be the work-around here ?