Start by doing you normal exim smarthost installation installation. Then make the following changes.
Edit the “/etc/exim4/passwd.client” file and insert your smarthost server name, smtp login and password. This will be used for the authentication. The smarthost server name has to match the settings you entered when doing the normal configuration.
Now edit the “/etc/exim4/update-exim4.conf.conf” file. This contains a line
Change this into
Now reconfigure and restart exim, this can be done with
and entering through all the options (unless you think some of the earlier settings need changing).
Now send a mail to test that your changes work.