No problem!
I was able to get the login to work. I thought I had to add the login url for saml, domain/auth/saml/index.php, but that didn't work. I removed the URL and left the field empty, we then got redirected to the login-page in Moodle where the users had to press the login.button for the SAML-integration.
The customer was happy with this solution, so I would say it works fine for us.
Thx Juan, for responding to my question.