Look at the
Vuelta Corsa HD wheelsets. They aren't light, but your friend isn't light either. These would be pretty strong with 36 spokes. I don't know if he could get just a rear wheel somewhere, but the set is just over two Benjamins. You didn't mention the spoke count on his front carbon wheel, but if it's a low spoke count (it probably is) then he might be better off riding something like these Vueltas for a while until he gets his weight down.
For what it's worth, I built
my own custom carbon wheelset that is something one simply cannot find on the open market, ie: nice semi-deep section carbon rims with high quality hubs, but with 36 spokes both fore and aft. Nobody makes something like this. It's awesome, but much more expensive than something like the Vueltas linked above.
One more thing to consider would be talking to a custom wheelbuilder. It would probably cost more than just buying off the shelf, and may not be worth it if this is seen as some kind of temporary solution until he's got more weight off. But consider that if your friend is at 290 lbs now the likelihood that he's ever going to get down to "typical" cyclist weight (say, 160-180 lbs) is pretty minimal, so having a strong wheelset is always going to be a concern. Even if he gets down to 230-240 or so he's still going to want stronger wheels than the typical skinny cyclist.
Edit: I had a look at some photos of that 2006 Jamis Sputnik bike, and I wouldn't hold out hope with that fork and rear frame of supporting very wide tires, but definitely he'll want to ride the widest tires that will fit. 25mm should be pretty easy, but if he can fit a 28mm (or higher) he'd be well advised to do so.