Exim, горячий для маршрутизации местной почты по другому адресу

The debug output you are using indicates you're using a Debian style configuration system. I'm going to refer to this as exim4 in order to make it clear that there is some extra configuration magic occurring beyond the default exim config that comes in the source. Anybody reading this later needs to clearly understand that some of this suggestion does not apply unless they are running Debian style exim configs.

The difference in your -bt output gives a clue:

root@srv02:~# exim -bt root@localhost
R: system_aliases for root@localhost
R: dnslookup for mypersoaddress@gmail.com
mypersoaddress@gmail.com

root@srv02:~# exim -bt root
R: dnslookup for root@mydomain.com
root@mydomain.com

In the first one, it knew to look in the system_aliases router because "localhost" is configured to be one of the domains that is allowed to look in the aliases file. But in the second one, it skipped over that aliases file because "mydomain.com" is not in that list. In exim4, that list is the MAIN_LOCAL_DOMAINS macro.

By my estimation, one of these things is probably going to solve your problem. Items 2 and beyond are potential adjustments to your exim.conf. Since you run exim.4, you need to be adjusting Debian mail configuration files in /etc/exim/ and then run exim4-conf.conf or something like that to have those changes read in and generate the new configuration file (/var/lib/exim4/config.autogenerated*) that exim4 actually uses.:

1. Make sure that the /root/.forward file is readable by the exim user.
2. Add mydomain.com to the list of domains called +local_domains which should then make exim4 look for the $HOME/.forward file. It does sound like you already have this set correctly.
3. Move the userforward router to occur before the dnslookup router (which it already does, but maybe you have changed the default router layout?)
4. Add mydomain.com to the list of domains allowed to search the aliases file. (likely this will break other things)