I'm sorry, but I'm using recomended SMTP as mailer in Horde configuration.
We also using IMAP server not POP3.

Don't use sendmail.  This is explicitly mentioned in the configuration 
documents.  It is impossible to reliably do error handling.  Use SMTP.

The entry looks fine, though you should NEVER add a complete backend 
configuration into backends.local.php, unless you absolutely need to.
I'm not sure if logging works on POP3 connections too though.

I'm sorry to late.

I try enable debuging on our server but without success.

My backends.local.php look like this:

$servers['pop'] = array(
     'name' => IMAP Server',
     'hostspec' => 'localhost',
     'hordeauth' => false,
     'protocol' => 'imap',
     'port' => 143,
     'secure' => false,
     'maildomain' => 'ecn.cz',
     'realm' => 'ecn.cz',
     'cache' => true,
     'preferred' => 'true',
     'debug' => '/tmp/imp_imap.log',
     'debug_raw' => true,
     'smtp' => array(
         'auth' => false,
         'debug' => '/tmp/imp_imap.log',
         'debug_raw' => true,
         'host' => 'localhost',
         'localhost' => 'smtp.ecn.cz',
         'port' => 25,
     ),
);

,but debug file is empty.

I was looking to my maillog and there are relevant lines:
Sep 27 21:10:43 ecn4 sendmail[8933]: r8RJAhvN008933: <">"@ecn.cz>... 
User unknown
Sep 27 21:10:43 ecn4 sendmail[8933]: r8RJAhvN008933: 
from=<jiri.reischig@ecn.cz>, size=0, class=0, nrcpts=1, 
msgid=<201309271910.r8RJAhvN008933@ecn4.ecn.cz>, proto=ESMTP, 
daemon=MTA, relay=ecn4.ecn.cz [89.250.245.71]


Please, send me more information how can I make debug file from IMP.

This sounds extremely unlikely.  A malformed address should have no 
bearing on the rest of the message body.

I can't actually test this locally, since my local SMTP server will 
decline the message as it interprets '>' as a local user name, and 
that user doesn't exist.  At a minimum you need to provide an SMTP log 
(see imp/config/backends.php).

For the record, ">" is a valid e-mail address.  By itself, it means 
the local user named >.  (A bare >, without quotes, is NOT a valid 
e-mail address.  But this is correctly caught by our parser and 
rejected).

IMP send empty email if one of recipient is ">".
It's not good email address, but the email is send empty for others 
well formated email addresses.
Example recipients list:
  john.doe@com.com, ">"