Changes have been made in Git (master):

commit 72e0459148572474ed0b3de805b4049849b59e64
Author: Michael M Slusarz <slusarz@horde.org>
Date:   Wed Nov 28 01:02:59 2012 -0700

     [mms] Another workaround for broken Cyrus APPEND behavior (Bug #11769).

  framework/Imap_Client/package.xml |    4 ++--
  1 files changed, 2 insertions(+), 2 deletions(-)

http://git.horde.org/horde-git/-/commit/72e0459148572474ed0b3de805b4049849b59e64

Marking as fixed in Horde_Imap_Client 2.2.3.

It works for me with commit 960691b5754d8ccd23cadaabb076cf72c231971f
Thanks a lot as this issue was really annoying.

One of the issues here is that there appears to be at least *2* 
different ways Cyrus is broken.  At least one version issues an 
untagged BYE response and another version issues a tagged UNKNOWN-CTE 
NO response.

This is a Horde_Imap_Client issue.

You can just patch the file.  Right now, the patch in this ticket is 
the only change re: this issue since the last Horde_Imap_Client release.

As I wrote, I'm using the latest stable release of Horde Groupware 
5.0.2. Is it possible to test your fix by only updating the one file 
you changed in the git-version? Or do I have to upgrade all of my 
packages to the latest git (which is not really an option for me)?

Changes have been made in Git (master):

commit f8faf517a6d68dd979b4b6df69f8eb6efdfb0f5d
Author: Michael M Slusarz <slusarz@horde.org>
Date:   Tue Nov 27 15:05:36 2012 -0700

     Another attempt at fixing Cyrus issue (Bug #11769).

  .../Imap_Client/lib/Horde/Imap/Client/Socket.php   |   15 ++++++++++-----
  1 files changed, 10 insertions(+), 5 deletions(-)

http://git.horde.org/horde-git/-/commit/f8faf517a6d68dd979b4b6df69f8eb6efdfb0f5d

Sending mails works but the mail is not saved in the sent-mail folder. 
There is also a thread on the mailing-list concerning this problem.

I'm using Debian squeeze and cyrus-imapd-2.2 Version: 2.2.13-19+squeeze3

Horde-Log:
2012-11-27T21:02:56+00:00 INFO: HORDE [imp] 37.24.25.81 Message sent 
to Jens Gruentjes <jens.gruentjes@provider.de> from jens [pid 3822 on 
line 875 of "/var/www/horde/imp/lib/Compose.php"]
2012-11-27T21:02:56+00:00 ERR: HORDE [imp] Der E-Mail-Server konnte 
den Inhalt der Nachricht nicht auswerten. Can not process the binary 
data [pid 3822 on line 390 of "/var/www/horde/imp/lib/Imap.php"]
2012-11-27T21:02:56+00:00 DEBUG: HORDE  1. 
Horde_Core_Ajax_Application->doAction() 
/var/www/horde/services/ajax.php:56
  2. call_user_func() /usr/share/php/Horde/Core/Ajax/Application.php:155
  3. IMP_Ajax_Application_Handler_Common->sendMessage()
  4. IMP_Compose->buildAndSendMessage() 
/var/www/horde/imp/lib/Ajax/Application/Handler/Common.php:536
  5. IMP_Imap->append() /var/www/horde/imp/lib/Compose.php:928
  6. IMP_Imap->__call() /var/www/horde/imp/lib/Compose.php:928
  7. Horde_Core_Ajax_Application->doAction() 
/var/www/horde/services/ajax.php:56
  8. call_user_func() /usr/share/php/Horde/Core/Ajax/Application.php:155
  9. IMP_Ajax_Application_Handler_Common->sendMessage()
10. IMP_Compose->buildAndSendMessage() 
/var/www/horde/imp/lib/Ajax/Application/Handler/Common.php:536
11. IMP_Imap->append() /var/www/horde/imp/lib/Compose.php:928
12. IMP_Imap->__call() /var/www/horde/imp/lib/Compose.php:928
13. call_user_func_array() /var/www/horde/imp/lib/Imap.php:388
14. Horde_Imap_Client_Base->append()
15. Horde_Imap_Client_Socket->_append() 
/usr/share/php/Horde/Imap/Client/Base.php:1811
16. Horde_Imap_Client_Socket->_sendLine() 
/usr/share/php/Horde/Imap/Client/Socket.php:1557
17. Horde_Imap_Client_Socket->_getLine() 
/usr/share/php/Horde/Imap/Client/Socket.php:3649
18. Horde_Imap_Client_Socket->_responseCode() 
/usr/share/php/Horde/Imap/Client/Socket.php:3824
2012-11-27T21:02:56+00:00 DEBUG: HORDE [imp] Nachricht wurde 
erfolgreich versendet, aber nicht in Gesendet gespeichert. [pid 3822 
on line 27 of 
"/usr/share/php/Horde/Core/Notification/Handler/Decorator/Hordelog.php"]

Imap-Log:
<1354050176<2 APPEND "INBOX.sent-mail" (\seen $mdnsent) ~{627+}
<1354050176<Date: Tue, 27 Nov 2012 21:02:56 +0000
Message-ID: <20121127210256.Horde.3umCTqN7arH5lvhY92DpwQ1@mail.xxx.de>
From: Jens =?utf-8?b?R3LDvG50amVz?= <jens.gruentjes@xxx.de>
To: Jens Gruentjes <jens.gruentjes@provider.de>
Subject: Test
Received: from ip-xx-yy-zz-zz.unitymediagroup.de
  (ip-xx-yy-zz-zz.unitymediagroup.de [xx-yy-zz-zz]) by mail.ebira.de (Horde
  Framework) with HTTP; Tue, 27 Nov 2012 21:02:56 +0000
User-Agent: Internet Messaging Program (IMP) H5 (6.0.2)
Accept-Language: de,en
Content-Type: text/plain; charset=UTF-8; format=flowed; DelSp=Yes
MIME-Version: 1.0
Content-Disposition: inline

Test
Message-ID: BAD Unrecognized command
From: BAD Unrecognized command
To: BAD Unrecognized command
Subject: BAD Unrecognized command
Received: BAD Unrecognized command
* BAD Invalid tag
* BAD Invalid tag
User-Agent: BAD Unrecognized command
Accept-Language: BAD Unrecognized command
Content-Type: BAD Unrecognized command
MIME-Version: BAD Unrecognized command
Content-Disposition: BAD Unrecognized command
* BAD Invalid tag
* BAD Invalid tag
* BAD Invalid tag
* BAD Invalid tag
<1354050177<3 STATUS "INBOX" (RECENT)
3 OK Completed
<1354050177<4 STATUS "INBOX.mailinglists.debian-sec" (RECENT)
5 STATUS "INBOX.mailinglists.horde" (RECENT)
6 STATUS "INBOX.mailinglists.niederrheiner" (RECENT)
7 STATUS "user.eug" (RECENT)
C64 UNSELECT
4 OK Completed
* STATUS INBOX.mailinglists.horde (RECENT 0)
5 OK Completed
* STATUS INBOX.mailinglists.niederrheiner (RECENT 0)
6 OK Completed
* STATUS user.eug (RECENT 0)
7 OK Completed
C64 BAD Please select a mailbox first