Problem solved.
May be I can help other people with the below information.
Problem wasn’t the Elementor functionality or META tags regarding “Open Graph Protocol (OGP)” but the (free) HTTPS “Let’s Encrypt certificate”!!! LinkedIn is the only platform who doesn’t accept this free security certificate, because the Elementor share button worked splendid for Facebook, Google+ and Twitter … ??
If you use a paid certificate (like Comodo) the problem should be solved.
Hope this helps.
Kind regards,
André