Oswald's cash

[Bill Brown]

He wasn't pretending to be anyone other than Lee Harvey Oswald, so "changing his appearance" between the lunchroom encounter and the encounter with Mrs. Reid, and then changing again before entering the bus, seems far-fetched. It's not clear to me what he would have gained by those gyrations. I can definitely understand changes at the rooming house - in fact, much bigger changes than he actually made (fake beard? Dallas Cowboys jacket?) if he'd really been planning ahead. My scenario has him in his white V-neck t-shirt during the shooting, slipping into his brown overshirt as he left the sixth floor, and Mrs. Reid simply not being a reliable witness. I don't know how many times I've spent all morning with my wife and then ended up looking for her in some store while thinking "What the hell was she wearing?"

My scenario has him in his white V-neck t-shirt during the shooting, slipping into his brown overshirt as he left the sixth floor...

Yes and Oswald most likely used the brown overshirt to wipe down the rifle as he made his way across the sixth floor which resulted in microscopic fibers lodging from the shirt into the crevice between the metal butt plate and the wooden stock of the rifle.  These fibers were later found to match the shirt fibers.

Then, once the rifle is wiped down and hidden, Oswald puts the brown overshirt on as he descends the stairs.