I've been thinking about doing this! I think it is very possible, because they are roughly similar sizes. It seems most people don't understand you question.... When I get around to trying it, I'll let you know if it works. Good luck if you try.
I'm not too familiar with cramming consoles into each other, but i imagine with a bit of cleverness, it might be possible to fit a DS lite into the oldschool gameboy, but i don't see that as particularly useful. Especially since the button layout would have to change pretty drastically, which might make it kinda awkward to use.
When I first thought about it, I thought it would work best if the GB was gutted and some kind of hinge was made between the front and back covers and that the guts of a DS were placed in the respective sides. That way it would still open and close like a DS. And when it was closed it would look like a GameBoy.
An original only has 1 screen, I'd love to see a creative (and not horribly ugly) resolution for that. One screen on top, one on bottom? Also, DS screens are rectangular, wider then tall. They may take up a good portion of the body, and leave little room for buttons. Maybe keeping the screens extremely close, and small buttons on the bottom. Any how this is done, it would be one of the coolest DS mods.
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Acually, why not try this? Cut the original frame in 2, put a hinge on it and make it flip like the DS/lite.