Which is your email provider (in case it has some particularities) and what are your account Copies & Folders settings for saving copies of sent messages?

The email provider is web.de (german provider), the setting for saving copies of sent messages is attached (please check the attachement). If I switch to an POP3 Account is it working. Just not with IMAP.

You have the settings for a copy to be saved - it looks like - in your online mail client but as storage. Using the radio button for the top option should save a copy in your Sent Folder. Try it with a test email and see what happens.

I tried it but with the same result. Email was sent but no copy at the sent folder.

Which 'sent' folder are you talking about? In the settings, it would be saved in your online sent folder.

I changed the folder to the local folder. now it works :-).

Thank you!

Well, you've "solved" the problem that way for the same reason it worked with POP, i.e. because you're storing your sent mail locally on your computer now, not on the server. Is that what you want? Because if not and you want your sent mail to be stored on the server, so you may also see it from e.g. webmail, then your problem is not solved…

I changed the folder to the local folder. now it works :-).

As per DavidGG's post. This is more a masking of the problem rather than a resolution. With an IMAP account, you really want the sent items to be in your Sent Folder online so that it is mirrored in the IMAP Account section of Thunderbird - not in a local folder.