Did you look at the actual sender of the dead message?  is the from field a valid senders?

The senders name is determined by the router from the message and then compared to the users entry in the address book... This will look formultiple cofigurations of the senders name, if the name is not found, then it is not a valid user, or there may be an issue with the users person document.  You can ry t refresh the routher tables (Tell router update config) and see if this clears up the issue.

Maybe I was not clear enough in my question.

The problem is not about dead messages, but the format of system messages, sent by Domino server. The mails are being sent with from address in format "dominoservername/domain", what is not valid Internet mail address and is rejected f.ex. by outlook.com.

And the question: is there any way to specify valid internet address for "From" field for Domino system messages?  It's possible to specify message content in server configuration, but not other parts of message.

Is ir just outlook.com?  Are messages to all other domains ok?   If just outlook.com do you have a special routing to that domain, like connection docs?  Look at Foreign SMTP domain document for one that is good and for the route this particular domain this is routing through

Outgoing messages are working correctly.

The problem is only with system messages, composed by Domino server itself. And the only problem is sender's incorrect interenet mail address, handled as spam by outlook.com and maybe some more mail servers. 

So the sender is a server name.  Normally in a total notes  environment it would not be an issue. Since the server doc does not have an internet name there is no substitution that can be done for the sender email address.   One thing I can suggest it that you forward the emails to a mail in db and then write a resend agent that would forward the emails to the proper email address.   Either you can write these emails into mail.bo or make sure the signer of the agent has a internet email address in their person doc

Update.   Just a wild try.  Populate a field called internetaddress on the server doc on the sending server and see if the router actually does the conversion,

Do you mean the SMTPFullHostDomain field which normally would be populated? 

It is not on the form   I just suggest add the field  to the actual doc (check the person doc for actual field name) using a simple agent.   I think it might show in the $user view   If it does then the router possibly might be able to do the translation from server name to internet name for the email from field.   If that does not work then as I suggested get the emails to a a db with a agent to re write the from field .  This can be accomplished with a mail rule on the server doing sending to outlook .com with a contains(fro;patter to indentify server) move to db

Hello

You need to create a global domain document and configure conversions

Configuration---Messaging---Domains

add domain

Global domain

etc