The problem is that according to Frazier's testimony the light gray jacket (CE 162) was worn by Oswald during the trip on Thursday evening to Irving. The fact that he wore the blue/gray jacket (CE 163) to work on Friday morning, which means that the light gray jacket stayed behind at Irving.
So, how did the light gray jacket get from Irving to the rooming house?
FBI Report 12/2/63
"At about 4:45 PM, on November 21, 1963, FRAZIER and OSWALD departed the TSBD building, walked to FRAZIER'S car, and drove to Irving. OSWALD did not have a package and was not carrying anything with him at that time. As FRAZIER recalls, OSWALD was wearing a reddish shirt and a gray jacket, waist length."
From Frazier's WC testimony
Mr. BALL - On that day you did notice one article of clothing, that is, he had a jacket?
Mr. FRAZIER - Yes, sir.
Mr. BALL - What color was the jacket?
Mr. FRAZIER - It was a gray, more or less flannel, wool-looking type of jacket that I had seen him wear and that is the type of jacket he had on that morning.
Mr. BALL - Did it have a zipper on it?
Mr. FRAZIER - Yes, sir; it was one of the zipper types.
...
Mr. BALL - Was it light or dark gray?
Mr. FRAZIER - It was light grey.
It is clear that Frazier testifies to Oswald wearing a grey jacket to Irving on the evening of the 21st and that he was wearing a light grey jacket when he went to work on the morning of the 22nd.
Nobody recalls seeing Oswald leaving the TSBD so do not know what he was wearing.
McWaters recalls the man who got on the bus was wearing a "little old jacket".
Whaley testifes that Oswald was wearing "some type of jacket".
Is it the case the only person who believes Oswald was wearing a shirt when he got back to the rooming house was Earlene Roberts?
If this is indeed the case we can assume Roberts was mistaken as she wasn't paying attention and two people have already testified that Oswald was wearing a jacket before he reached his rooming house.
Oswald wore his light grey jacket to Irving on the 21st.
He wore the same jacket to work on the 22nd.
He left work wearing the same jacket.
He got back to his room wearing the same jacket.
He left his room wearing the same jacket.
BS. You can not assume that Oswald ditched a jacket unless you demonstrate first which of the two jackets he owned it was.
The blue/gray jacket was found at the TSBD and the light gray jacket was, according to Frazier, worn by Oswald to Irving on Thursday evening. There is no way that light gray jacket could have gotten from Irving to the rooming house.
How can Oswald ditch a jacket if he did not have one to put on in the first place?
Oswald entered the rooming house wearing his light grey jacket and left wearing the same jacket.
He was not wearing it in the Texas Theater