thanks for the reply
I did some checks and not really any further in solving my Problem:
according to SSL Labs the site is rated with an A
according to LinkSpy: The SSL setup for this website is absolutely flawless and does not negatively affect rankings
according to the Really Simple SSL Wordpress Plugin:
success SSL is enabled on your site.
success Mixed content fixer was successfully detected on the front-end
success An SSL certificate was detected on your site.
success https redirect set in .htaccess
success HTTP Strict Transport Security was set in the .htaccess
= Your site is not yet configured for the HSTS preload list. Read the documentation carefully before you do! Enable the preload list
= The mixed content fixer is not active on the admin panel. Enable this feature only when you have mixed content on the admin panel.
success The native Wordpress function is_ssl() returned true
success Great! Your scan last completed without errors.