Once you have the selection ready on the first image,
use the move tool (refer the below screen shot for the moov tool) and then drag the selection from first image to the secon image tab.
As soon as you will place the cursor on the second image tab the second image will open up and now you can place the cutout on the second image.
It will create the layer for you automatically.
YESSSSSS!!!!! Thank you so much. That was exactly what I've been trying to do. Using the move tool was something I had missed (if it was there...) in all the tutorials and guides I had red. Very much appreciated.
You can also copy the selection to the clipboard (Edit > Copy), open the destination picture, and paste from the clipboard (Edit > Paste).