I actually did this yesterday, and wouldn't say I'm a super-strong guy or anything. The way I did it was to rotate the grill body back on top of the box/pallet (with cushioning). I then attached the cart horizontally and levered it up, which was actually fairly easy (make sure you lock the casters first). Toughest part was reaching around some weird angles to tighten the nuts.
Also, make sure you take everything you can out of the grill before doing this - saves a bunch of weight.
I wish I could take credit for thinking of this myself, but its actually how the Smokefire was assembled.