since my provider has update his certificate, I get the following Error:

But if I check the server ‘mail02.stuenings.de’ on the website ‘https://www.digicert.com/help/’, the certificate is ok.

K-9 Mail Version is 5.600

It’s possible your phone is missing the CA root for that particular cert. If you’re satisfied that the certificate is legitimate, you can press “accept certificate” and K-9 will remember that choice until the cert changes again.