Your comments

Made 2 tests and all mail delivered. (Though with a 3 minute latency, maybe something with the networks).
Thank you!!
It doesn't seem to work.
If I have a mailbox:  sorin@example.com I can't add a forward account with the same sorin@example.com mail.
Yeah.. Everything seems to work OK.
Until you get a first mail the when Thunderbird accesses the account it gives an error.. but then after it works.

Thank you very much for all your help with this issue!
I have manually created a forward email for the mailbox sorin@esgy.info .. with forward to gmail and it worked..
But accessing it through IMAP with thunderbid still doesn't work.
I've found something:

The results for this:  exim -d -bt sorin@esgy.info


>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Testing sorin@esgy.info
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Considering sorin@esgy.info
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
routing sorin@esgy.info
--------> vforward router <--------
local_part=sorin domain=esgy.info
checking domains
esgy.info in "esgy.info : localhost"? yes (matched "esgy.info")
esgy.info in "+local_domains"? yes (matched "+local_domains")
R: vforward for sorin@esgy.info
calling vforward router
rda_interpret (file): /etc/exim.forward/$local_part@$domain
expanded: /etc/exim.forward/sorin@esgy.info
/etc/exim.forward/sorin@esgy.info does not exist
checking parent directory
stat(/etc/exim.forward/.)=0
/etc/exim.forward/sorin@esgy.info does not exist
vforward router declined for sorin@esgy.info
"more" is false: skipping remaining routers
no more routers
sorin@esgy.info is undeliverable: Unrouteable address
search_tidyup called
>>>>>>>>>>>>>>>> Exim pid=13867 terminating with rc=2 >>>>>>>>>>>>>>>>


I have only a mailbox: sorin@esgy.info
I can't add a forward with the same address. I tried but it fails.

I added a forward mailobx and tested it with: exim -d -bt sorin2@esgy.info

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Testing sorin2@esgy.info
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Considering sorin2@esgy.info
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
routing sorin2@esgy.info
--------> vforward router <--------
local_part=sorin2 domain=esgy.info
checking domains
esgy.info in "esgy.info : localhost"? yes (matched "esgy.info")
esgy.info in "+local_domains"? yes (matched "+local_domains")
R: vforward for sorin2@esgy.info
calling vforward router
rda_interpret (file): /etc/exim.forward/$local_part@$domain
expanded: /etc/exim.forward/sorin2@esgy.info
20 bytes read from /etc/exim.forward/sorin2@esgy.info
file is not a filter file
parse_forward_list: forapathy@gmail.com,
extract item: forapathy@gmail.com
vforward router generated forapathy@gmail.com
errors_to=NULL transport=NULL
uid=unset gid=unset home=NULL
routed by vforward router
envelope to: sorin2@esgy.info
transport: <none>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Considering forapathy@gmail.com
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
routing forapathy@gmail.com
.......



Hope it helps....
Currently I could add the account in Thunderbird.. it connected successfully but fails with "Unable to open this mailbox".
I can send emails. I tested with: echo "test mail." | mail -s Test email@example.com

But any email sent to the email box on this server fails with the error above "Unroutable address".
I didn't get this before the update.. Maybe I still need to configure something more...

Thank you!

I've sent an email with the attachemnts!
2014-05-26 18:07:44 1WozJI-0001zj-Nl <= email@gmail.com H=(mail-ve0-f172.google.com) [209.85.128.172] P=esmtp S=1755 id=CAC+UjKiNsdA-cBWQYZuX5jFp8M3WwhHvVqx9=i7frFb3vNBW0Q@mail.gmail.com
2014-05-26 18:07:44 1WozJI-0001zj-Nl ** sorin@email.info: Unrouteable address
2014-05-26 18:07:44 1WozJI-0001zm-SI <= <> R=1WozJI-0001zj-Nl U=Debian-exim P=local S=2544
2014-05-26 18:07:44 1WozJI-0001zj-Nl Completed
2014-05-26 18:07:45 1WozJI-0001zm-SI => email@gmail.com R=dnslookup T=remote_smtp H=gmail-smtp-in.l.google.com [74.125.136.26] X=TLS1.2:RSA_ARCFOUR_SHA1:128
2014-05-26 18:07:45 1WozJI-0001zm-SI Completed


(I will edit later to remove the actual emails)

Update: edited emails
I've made the upgrade then deleted the old emails and created 2 new email.. One mailbox sorin@example.com 
and one for forwarding  sorin2@example.com..

Both fail with message: 
The error that the other server returned was:
550 Unrouteable address

I have updated ajenti mail

I have no AAAA record, just an MX record.
Ajenti was installed on a fresh Debian7 installation and no changes to IP were made.

Now I get "email@example.com Unrouteable address" in mailog when I send an email to the account.