Normally the dropouts in the frame where the wheel screws in are different depending on if the bike uses a sprocket cluster or an internal hub gear - there is almost certainly a workaround somehow, somewhere, if you really had your heart set on swapping. Mucking around with bikes is a great way to learn, but it's often the hard way and any special adapters and connectors you might need tend to add up.

You would also need a new rear brake on the pink folder to replace the coaster brake the hub has now.

Ih it were my decision I'd keep the Duomatic just where it is. It's far nicer than than the Positron anyhow.