This Problem is solved too.
It happens when the mail folder on the system doesn't exists.
Just create the folder for the specific user and let the mail user own it.

Fixed that by editing horde/imp/backends.php
$servers['imap']  hordeauth to 'full'

But now i got a exception which says that the socket connection is null
2013/08/22 13:51:29 [error] 26701#0: *360 FastCGI sent in stderr: "PHP 
message: PHP Fatal error:  Call to a member function write() on a 
non-object in /usr/share/php/Horde/Imap/Client/Socket.php on line 3959
PHP message: PHP Stack trace:
PHP message: PHP   1. {main}() /var/www/horde/services/portal/index.php:0
PHP message: PHP   2. Horde_Registry::appInit() 
/var/www/horde/services/portal/index.php:15
PHP message: PHP   3. Horde_Registry->__construct() 
/usr/share/php/Horde/Registry.php:246
PHP message: PHP   4. 
Horde_Core_Factory_Notification->addApplicationHandlers() 
/usr/share/php/Horde/Registry.php:525
PHP message: PHP   5. Horde_Registry->listApps() 
/usr/share/php/Horde/Core/Factory/Notification.php:52
PHP message: PHP   6. Horde_Registry->hasPermission() 
/usr/share/php/Horde/Registry.php:897
PHP message: PHP   7. Horde_Registry->isAuthenticated() 
/usr/share/php/Horde/Registry.php:1664
PHP message: PHP   8. Horde_Core_Auth_Application->transparent() 
/usr/share/php/Horde/Registry.php:2163
PHP message: PHP   9. Horde_Registry->callAppMethod() 
/usr/share/php/Horde/Core/Auth/Application.php:366
PHP message: PHP  10. call_user_func_array() 
/usr/share/php/Horde/Registry.php:1174
PHP message: PHP  11. IMP_Application->authTransparent() 
/usr/share/php/Horde/Registry.php:1174
PHP message: PHP  12. IMP_Auth::transparent() 
/var/www/horde/imp/lib/Application.php:367
PHP message: PHP  13. IMP_Auth::authenticate() 
/var/www/horde/imp/lib/Auth.php:118
PHP message: PHP  14. IMP_Imap->login() /var/www/horde/imp/lib/Auth.php:87
PHP message: PHP  15. IMP_Imap->__call() /var/www/horde/imp/lib/Auth.php:87
PHP message: PHP  16. call_user_func_array() 
/var/www/horde/imp/lib/Imap.php:571
PHP message: PHP  17. Horde_Imap_Client_Base->login() 
/var/www/horde/imp/lib/Imap.php:571
PHP message: PHP  18. Horde_Imap_Client_Socket->_login() 
/usr/share/php/Horde/Imap/Client/Base.php:767
PHP message: PHP  19. Horde_Imap_Client_Socket->_tryLogin() 
/usr/share/php/Horde/Imap/Client/Socket.php:435
PHP message: PHP  20. Horde_Imap_Client_Socket->_se

The Permission validation for IMP isn't working correct.

Steps I did:
1. install horde with all deps and binaries from pear
2. configure horde
3. install imp
4. configure imp
5. add group "imp"
6. add permission "imp" for group "imp" with all privileges on imp app
7. try to login to imp

The function call $registry->pushApp in /Horde/Registry.php:253 throws 
a AUTH_FAILURE exception.
In the log i can see that the authentication is successful but when 
the app tries to select the preferences which are not there the login 
fails.
SELECT pref_name, pref_value FROM horde_prefs WHERE pref_uid = 
'email@host.de' AND pref_scope = 'imp'

The prefeferences are not created for this user.
The mail server i installed has this components: postfix, sasl, 
courier, pam, mysql and its working and running.