I know of only one Oswald who shot killed JFK on 11/22/1963. He killed a cop that same day.
Apparently one of the supposed fake Oswalds (there were two? three? six? as many as needed?) went to work with Frazier that day, worked all morning at the building, shot JFK, then left. And nobody realized it wasn't the real Oswald.
In conspiracy world nothing has to make a lick of sense. It just has to somehow support a conspiracy. What conspiracy is that? Any one will do. Or two. Or four. They can all contradict one another, make no logical sense, be at odds with each other: it doesn't matter. In fact, the more complex the better.
Tom Bethell, who had worked for Garrison early on but quit in disgust with what he (Garrison) was doing, explained the thinking behind the multiple Oswald idea:
"The extraordinary complexity involved – three Oswalds! -- is a fundamental characteristic of conspiratorialist reasoning. Philosophers like to point out that any belief, more or less, can be sustained if the believer is willing to encrust his belief with enough assumptions; the only problem is that the resulting theory starts to look very complicated compared to much simpler alternatives readily at hand. It is an important principle of philosophy (although one little valued in assassination conspiracy circles) that the simple explanation should be preferred to the complicated one.
Consider another famous case. Is the earth round or flat? It is possible to argue that it is flat and yet maintain an appearance of rationality. I once went to a lecture given by a member of the Flat Earth Society, and it was surprising how similar his reasoning was to that of the various conspiracy theorists I have known. A Flat-Earther, for instance, is likely to tell you that the moon landings never really took place, that NASA is collaborating with the CIA to deceive the Russians and the American people. . . . Sound familiar? To believe the earth is flat one must also believe that a large number of people are working assiduously to deceive our minds, and it is, in the end, just so much simpler to conclude that this conspiracy does not exist.
But your average conspiratorialist sees little merit in the argument from a standpoint of simplicity. To accept the simple explanation, he feels, is just simple-minded. Somehow conspiracy theorists seem, above all, determined never to be accused of being naive. Gore Vidal gives this impression in his condescending reference to "most Americans being quite at home with the batty killer who acts alone in order to be on television." Jones Harris, rather than drop back down to the simple and perhaps rather "naive" hypothesis of one Oswald, tries to rescue the shaky two-Oswald theory by adding on another Oswald.