After some of the users have been switched the outgoing queue on Exchange server is rapidly filli (4351481)

Some of the users have been migrated, their mailboxes have been synchronized and after switching their mailboxes mail flow stopped working for the entire organization.
When examining the outgoing queue on source Exchange server it is visible that there are thousands of messages and number is increasing, when examining the log it informs about failures, not authorized. Issue is partially caused because target Exchange 2007 server by default drops the connection as soon as there are more than 5 protocol errors. Increasing this setting is not desirable and doesn't really help.
When examining the messages it has been noticed that the sender field is blank and has no value.