I have to tread somewhat tentatively here for a couple of reasons:
a) My knowledge of rifles is minimal, I've never even held one let alone fired one. So there is a certain amount of guesswork going on.
b) What I'm going to point out is so obvious, it must have been brought up by someone researching the subject. It seems almost impossible this has gone under the radar for decades, which makes me think it must have been dismissed as an argument already but I just didn't get the memo.
So here goes nothing...
The telescopic sight on the Mannlicher Carcano purported to be Oswald's assassination weapon, is fitted on the left hand side of the rifle.
As I understand it, this makes it a rifle set-up for a right-hander. This doesn't necessarily mean the shooter was right-handed, just that he fired the rifle right-handed. This means his left hand would grip the stock, the rifle butt against his right shoulder and his right hand on the trigger. The shooter would lower his right eye to the scope and as he did so his head would tilt to the right.
This is the important part to remember, that the assassin's head would tilt to the right as head lined up the shot.
It's important to remember because there is first-hand eyewitness testimony that, at the time of the shots, the assassin tilted his head to the left as he was looking down the rifle.
On another thread I posted a list of the available evidence about who was on the 6th floor just before, during and after the assassination and that all the evidence points away from Oswald as being the assassin. One of the pieces of evidence is the testimony of Amos Euins. Over and over again young Amos insists the shooter had a "bald spot" on his head, he must say it about seven or eight times. Not a receding hairline - a distinctive bald spot - which is something Oswald didn't have. It's something I've mentioned many times but never really thought about how Amos could see a bald spot on top of the head of someone stood on the 6th floor of the TSBD building. From his viewpoint, looking up to the Sniper's Nest, there is no way he could see the top of the assassin's head.
At this point in his testimony Euin's is describing watching the assassin as he fired at the motorcade:
Mr. Specter: All right. Now, when the third shot occurred, Amos, let me ask you again, where were you looking then?
Mr. Euins: I was still down here, looking up at the building.
Mr. Specter: What did you see in the building?
Mr. Euins: I seen a bald spot on this man's head, trying to look out the window. He had a bald spot on his head. I was looking at the bald spot. I could see his hand, you know the rifle laying across in his hand. And I could see his hand sticking out on the trigger part. And after he got through, he just pulled it back in the window.
He describes the assassin holding the rifle as he was shooting and that he could see the bald spot on his head because the assassin was "trying to look out the window". But what does that mean? Later on in the testimony, Euins is more specific:
Mr. Specter: Now, what kind of a look, if any, did you have at the man who was there?
Mr. Euins: All I got to see was the man with a spot in his head, because he had his head something like this.
Mr. Specter: Indicating his face down, looking down the rifle?
Mr. Euins: Yes, sir: and I could see the spot on his head.
During this part of his testimony Euins is explaining that he could see the assassin's bald spot because he "had his head something like this". Obviously we can't see what action he was performing but Specter clarifies it - "Indicating his face down, looking down the rifle", to which Euins replies affirmatively - "Yes, sir".
Euins is saying that he could see the bald spot on the assassins head because, as the assassin lined up the shot and brought his head down to the rifle, he tilted his head, exposing the bald spot on top of it for Euins to see.
If you think about Euins, think about him stood across from the TSBD building looking up at the 6th floor and think about the direction the assassin was shooting in, it becomes very clear that, in order for the assassin to have exposed the bald spot on his head to Euins as he lined up the shot, it must be the case that the shooter tilted his head to the left as he was looking down the rifle.
If the is the case, we know for a fact that the weapon being used was not the Mannlicher Carcano discovered on the 6th floor, as this was set up for a right-handed shooter whose head would have tilted away from Euins at the time of the shooting.
And if it wasn't the Mannlicher Carcano being used as the assassination weapon then we have a conspiracy!
If we return to Euins' testimony from earlier he describes seeing the rifle laying across the shooter's hands and being able to see "his hand sticking out on the trigger part". Elsewhere in his testimony he describes seeing "the trigger housing and stock and receiver group out the window."
If the assassin were right handed, this much of the rifle would have been obscured from Euins' viewpoint as it would have been hidden on the other side of the assassin's body. The only reason Euins could see so much of the rifle is because the assassin was left-handed and the rifle was on the side of his body facing Euins.
If everything I'm saying is correct then we have first-hand eyewitness testimony proving the assassination weapon was not the Mannlicher Carcano discovered on the 6th floor of the TSBD building. This fact alone would prove there was a conspiracy.