Hello, I posted this question to this board, because it looks to me, that WP core doesn't support this feature, I'm not sure if it should work, but it would be nice if someone with knowledge could clarify this.
All cases that I found on the internet deal with the new secondary menu that should be registered and used in a child theme. In my case I have a parent theme with two registered menus and I have a child theme, where I want to use both of them. There is no problem with the 'primary' menu, somehow even without registering it works in a child theme out of the box.
The problem is that secondary menu will not be generated when called from the child theme. For details please see this question at wp stackexchange:
Thank you!