Originally Posted by sykerocker

I'm going to recommend taking both those bikes apart, cleaning them (that Varsity stem/shifter area needs a oxalic acid bath BAD!) and then putting them back together as original. Some of the matters you're dealing with include:

Taking down and rebuilding the rear wheel on the folder. The folder is a 24" wheel. The Varsity is a 27". Even if in good condition, you're probably not going to be able to reuse the spokes, as the hubs are probably a different diameter. And, to do it right, you'll be rebuilding the front wheel, too. And . . . . . . have you measured the rear hub width and rear dropout width on the folder? I'm assuming the Varsity is 120mm.

Making the crank work. Does the folder have the same style Ashtabula crank as the Varsity? I'm assuming the Varsity doesn't have a front freewheel setup on the crank. If so, the bearing used in Schwinn one piece cranks are different from anybody else's one piece crank.

OK, let's say you've got the wheels swapped, and the Varsity crank working. Now, does the front derailleur from the Varsity even fit on the folder? Little matter of strapping it around the seat tube. If its a normal folder, I doubt it.

Then we get up to mounting the rear derailleur (is the right rear dropout amenable?) and the vagaries of the setup.

Obviously, it can be done. I have no doubt that I can do it. Then again, I'm a bicycle mechanic with 40+ years experience, a fully equipped shop on the other side of my driveway (I do vintage restorations professionally as a hobby-business), and the time, confidence, and patience that absolutely nothing cannot be done and there is no bicycle that cannot be fixed. Hopefully you share my experience (OK, five years experience would probably do it) and confidence before diving in.

Best off, just restore the bikes the way they were. You're going to have a wonderful learning experience that'll possibly set you down the path that I followed, and two nice bikes to ride when you're done. What you're not going to get, despite your dreaming, is a cheap answer to a Brompton, Bike Friday, etc. If you want a derailleur equipped folder, at least start off with a more modern frame that's designed for that kind of drivetrain. You're attempting the equivalent of adding a derailleur to a three-speed roadster like I did 40 years ago as my daily commuter. It worked, but the labor involved to make it work was more trouble than the final product was worth. I'd have been better off just buying a 10-speed commuter bike (Schwinn Suburban or Raleigh Sprite). And I was working from a commercially available conversion kit, not rolling my own from the moment go like you're proposing.