What I need is to make a copy of an object to another scene, but keep the object data the same (link).
There are at least 2 ways:
Select your object on the original scene, go in the Object menu > Make Links > Objects to Scene > then choose your other scene.
You could also create an object in the other scene, select it and go in the Properties panel > Data, and in the top dropdown menu (Browse Mesh Data to be Linked) choose the mesh you want.