2nd Testimony of Oswald's 'cab driver' Wm Whaley..
The cab driver had Oswald wearing a jacket before he ever [supposedly] put one on.
"It all came back to him" after some apparent persuasion [from somebody]
Whether Saint Oz was wearing a jacket or not when he was in the cab has no importance. Just like who found the jacket doesn't matter.
What does matter is if Saint Oz was wearing a jacket when he left his room.
If he was, then it's hard to understand why he no longer has a jacket when he's arrested.
The implication that the jacket that was found wasn't his, or was planted is pretty much destroyed by the fibers that matched his arrest shirt in the jacket and the fact that the conspirators would have had to known that Saint Oz wouldn't have had a jacket when he was arrested. The cops woud look pretty dumb arresting someone with a jacket when the suspect they were looking for discarded his after murdering JDT.
I know this is too much common sense for the Ozzie fanbois, but don't let common sense get in the way of your Oz worshipping.