Perhaps there is a plug in but I do not know of it.
Edit I am wrong You bring into focus the document you want to have the object change color and select it.
Then bring into focus the document with the object you wish to pick up the color from
then do not select that objectt but rather simply click with the eyedropper tool and drag the eye dropper tool on to the document that contains the object you wish to change color.
That should do it
I got it wrong again.
What you actually do is bring inot focu the document witht he object you want to change and selecct the object
then click the object with the eyedropper tool and hold the mouse down and drag iut to the document object with the color you want to bepicked up and that will do it.
Ah, yes it works now for me as well.
Newby discovery from me is that you have to open two documents in one window.
Don't work with tabs and one window to view one document. Bringing object to a tabbed document didn't work for me.
But go to icon: arrange windows and bring both documents visual for your eyes.
Edit: Didn't work for coloring mesh gradients though. I could only select the object and change color of entire object.