When I send messages off-line, they enter in the addressed mailbox with the date and hour which I've clicked “Send later”. How could I set up to the real time?

What you say about Send Later timestamp is correct.

When you click Send or Send Later a time is set regardless of when you actually sent the Send Later email.

Please voice your vote at this link: https://bugzilla.mozilla.org/show_bug.cgi?id=560901

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One opton to get around this. Save the email to Drafts folder. then later open the email from Draft folder and click on Send.