It's complicated afaik. I am not familiar with the new versions, but it's possible. If you try to start in the schematic, your board will be populated with parts that need to be replicated. If you start in the board editor, it'll just tell you to do it in the schematic.
IIRC, the way I've done it is to close the schematic, then copy/paste the block of parts and traces in the board editor. At this point, when you open the schematic, ERC will fail and annotation is broken. Copy/paste the corresponding block of parts/wires in the schematic, and then use ERC error report as a guide to rename segments and components. When ERC passes, you'll regain back-annotation. When you're replicating things like this, you might have to be careful to make sure that your new segments aren't all connected to the same nets as the old ones.
An alternative approach would perhaps be to replicate the block in the schematic editor, At this point, you'll have a pile of unconnected parts in the board editor. Go to the board editor, turn off component origins and replicate the relevant copper without the components. Then you should be able to place the pile of new components on the replicated copper, and rename the segments to match what the ratsnest expects.
I'm not sitting in front of Eagle atm, but this is my recollection. It's something along those lines.