HOW I DID IT:

The boxes have a thick plastic covering the opening, so I first removed the plastic from only one of the boxes. I slid my blade just in between the plastic and the box along all sides to loosen the glue, and it popped right out.

Then I pulled out the padding inside, turned it over and cut a long narrow opening, wide enough for the adaptor ends of my cords to fit through.

I also removed the pink ribbon on the back. That is my top box.

The bottom box I also ripped out the padding and removed the ribbon from the back.
I cut a matching opening in the bottom

And on the opposite side of the bottom box, I punched 3 holes for my cords to run through. After punching the holes, I made a slit from the hole to the edge of the lid with a razor blade, so that the cord can be pushed through the slit into the hole, and it will only look as if the cord is running through the hole itself.

Next I used craft glue to glue the two boxes bottom-to-bottom, lining up the narrow openings

And ran my cords through the bottom box and

up through into the top box.

I replaced the padding in the top box, leaving just the adaptors peeking over the edge.

And that was it! Remember that I took out the plastic on this top, so I can just reach in and plug in my phone or iPod and let it rest on the pink padding!