So can an Earth-like planet be the moon to a Jupiter for example? Or something of that size.

And just to be clear, the Earth-like planet comes with a lush world and EVERYTHING on earth included.
including human life.

Yes, it's possible. In fact some of the best candidates for life in the solar system outside of Earth include the moons of Jupiter and Titan of Saturn. These aren't lush worlds by any stretch - any life would have to exist in oceans heated by geothermal mechanisms miles below a thick crust if ice. But it does seem possible.

Sounds like you interested in something like the forest moon of Endor from the Star Wars movie "Return of the Jedi" (the third of the original Star Wars trilogy). Certainly it's possible.

Thank you again.
I have to say I really enjoy reading your answers more than anyone else's
They are efficient, sharp, to the point, and it seems you get my original meaning behind the question. Really great.

And yes something like the moon of endor is what is on my mind.

So can you please suggest anything that I need to know for such moon to work?

1. for example the size of both bodies.
2. distance
3. can there be 2 other moons? ( just rocks really )
4. and how would the orbit of such moon be ?? I mean to ask about the day and night cycles and seasons and year...