@Oliver Lietz I'm glad to see you were able to resolve your issue. Thanks for posting your solution so that others experiencing the same thing can easily reference this. Since the Microsoft Q&A community has a policy that the question author cannot accept their own answer, they can only accept answers by others, I'll repost your solution in case you'd like to Accept the answer.
. Issue:
You want to connect to skype channel from Azure Bot Service.
. Resolution:
- Copy the "Add to Skype" URL to the clipboard
- Insert the URL into the Skype app as a message to myself
- Click on the URL in Skype
**
Please do not forget to "Accept the answer” and “up-vote” so that it can be beneficial to other community members.