Please post a screenshot. http://support.mozilla.org/en-US/kb/how-do-i-create-screenshot-my-problem

This is how my screen lokks:

What is your account type, POP or IMAP? My best guess would be IMAP.

Yes, IMAP, attached the settings

A message is first sent to your provider's SMTP server. In a second step, the message is copied to the Sent folder. For most provider's this happens via IMAP, i.e. the message is transmitted again, this time to your provider's IMAP server. There are exceptions though, e.g. Gmail. They do everything in one step.

The first two boxes are self-explanatory, but my question was really about the third box: why is TB sending the log in information and to whom? Attached again a picture of the third box.

I'd say this is the login to the IMAP server.

Sorry, I have difficulty following you: why would TB send login information for the IMAP server in the third step AFTER it had already sent the message to the server in the first step. So it must have had access to the server before sending the login information.

Isn't possible to trace the sending process and find out what steps are executed? I, and I believe many other users, would like assurance that TB is not spreading our login information

Sorry, I have difficulty following you: why would TB send login information for the IMAP server in the third step AFTER it had already sent the message to the server in the first step.

I thought I had explained that. https://support.mozilla.org/en-US/questions/1115191#answer-858739

I, and I believe many other users, would like assurance that TB is not spreading our login information

Thunderbird certainly doesn't do that, and it wouldn't make any sense. I'm not a fan of conspiracy theories. If you think you do have any evidence that this is the case, please present that evidence. But speculating of what you believe may happen doesn't help anyone.

Wrt to logging, feel free to do that. http://kb.mozillazine.org/Session_logging_for_mail/news