I'm looking for a way to make a private live broadcast, for example: From laptop A to Smartphone B. Is something possible even without other people watching?
Definitely.
Depending on what you want, you can use conference software like NetMeeting, etc. (there's a lot of free stuff) or you can do something like a twitch stream that you do not make public.
No, it should not be a public private stream like youtube, twitch and co. Only from A to B.
Then there's only one software solution.
As I said, depends on what should happen… But I guess, if you googlest for conference software is sure to find something suitable.
A screen transfer via Skype works very well, at least between two PCs. With the mobile app that should theoretically be possible with a smartphone.
