He is hit in the back later - likely at z271-272 in my view - just before Greer turns around and just before he falls back onto Nellie, just as JBC and Nellie stated.
Given the position of JBC’s torso at that point in time, how do you propose that a bullet fired from the SE corner window of the sixth floor of the TSBD was able to enter his back near the right armpit and exit his chest just below his right nipple?
The bullet, essentially, went around most of the chest cavity and exited below the right nipple without passing through the right lung. Because Gov. Connally was twisted around, his armpit, fifth rib and right nipple were roughly on a line that did not pass through the lung. At z272, the car was moving almost directly away from Oswald so the shot was from almost directly behind.
The bullet struck the fifth rib and pushed it in (causing a fracture of the rib near the spine) and kept pushing it in farther as it travelled along the rib until it penetrated the rib destroying the last 10 cm of the rib and driving fragments into the lower lobe of the right lung. It may be that he had to be twisted right in order for the bullet to travel between the right armpit entry point and exit below the right nipple without going through the right lung.