I think,,it can copy and transfer poze and shape.
so it can not work as you hope,, when you select genesis and select copy from top menu or short cut key,
when load two genesis (or prop etc) in the scene,
you can copy genesis 1 poze and shape, tehn can paste(transfer) it genesis(2)
so you need to load two same object or same figure in the scene to use copy and paste of top menu,,,
there is no way,, just copy and paste (it means load copied figure in the scene,I think,,)
but there is node instance.
may you try and check,,
select genesis or prop, then from top menu create>node instance or node instances..
they can only copy the figure or prop shape as instance, so you can not poze them,
butrotate or change scale or translate them.. you may understand easy how it work,,
maybe it is useful to make crowd scene,, or,, forest etc I think.
or,, save the item as scene subset from top menu, then load. It seems easy way