It may sound correct, but where exactly does this claim originate? Do stupid people traditionally have holes in their pockets? Do they throw money at trees and laugh? Because I can tell you, that is not nearly as much fun as it sounds. So are a fool and his money really so soon parted? To answer this question, Science and Googles have been combined to produce a question-answering chart.
A fool, represented by the blue line, first makes his appearance in the early 1500s. We can see that his money, represented by the red line, is not yet present. Possibly he is a court jester, perhaps paid in gruel. Certainly that is one explanation.
In 1560 his money begins to appear, although initially he is not around to enjoy it. Perhaps he is on vacation while his agent negotiates a better deal for him, one in which money features more prominently than gruel.
For much of the early 1600s he is again absent (gruel poisoning?) during which time his money continues to accumulate, so that by the time he does return in 1630 he is comparatively wealthy and can afford all the gruel his heart desires, although to be honest he's probably not the biggest fan of gruel at this point.
Now we see a surprising result: from this point onwards, a fool and his money have never been completely parted again. In fact, from 1700 onwards, a fool and his money have consistently kept pace with each other, and in fact seem to have gone hand in hand. A fool, it seems, is never short of gruel tokens.
In conclusion then: a fool and his money did indeed have a poor relationship initially, but in more recent times have been pretty much constant companions, probably due at least partly to a decreased expenditure on gruel.