Activity as a Groupjive Module

Correct me if I am wrong... if I would substitute the Activity-Tab in a module, i need to set the config to display "Everyone", right?

That's entirely up to you. If you use #displayedOrMe then when you're on a users profile other then your own it'll show their activity otherwise it'd show yours. If you set it to always show everyones activity then that also works too I suppose if that's what you want.

What do you mean by "module wrapper" ? Something like "Component2Module"..

Extensions > Module Manager > New > "Wrapper"

It shows a URL in an iframe. You'd simply supply the URL to the recent activity page.

Extensions > Module Manager > New > "Wrapper"

Aaah, you never stop learning :silly:
Although, i hate iframes
I guess, i am gonna try it with comp2module... remember that there was one extension without iframe.

Not sure how that'd work as CB Activity isn't a component; it's a CB plugin. I suppose if you had something that requested the URL and echoed the results that could work.