It can a bit tricky but what works for me:
1) Select the polygon, or polygons, that you want to copy across to another layer.
2) With your cursor still over the map view, with the map view active, right-click and choose Copy.
3) Then from the Map tab and Clipboard group, select the option to Paste Special.
4) Then select the required feature layer from the list of available editable options.
It is important to make sure that the map view is active, not the Contents pane or any of the other panes.