Fake. There are clear engineering issues that would arrise with this design. First, the jet engine would be assumed to be ahead of the cockpit slightly aft of the original radial engine. This would require a very long tail pipe for the engine resulting in a loss of thrust. It would also require a redesign on the rear half of the fuselage to widen it to take this exhaust.
The cockpit would be another issue. Would there be room beneath it for the exhaust? How would it be kept insulated from the heat generated by that exhaust?
Then there are serious CG issues. You've removed the turbosupercharger and all associated ductwork, put a much lighter turbojet in the plane instead of a piston engine, and made other changes as well, such as--at least in the picture--added in a bunch of weight forward in armament and ammunition while removing this (I assume) from the wings.
Then there's the fuel issue. Turbojets consume far more fuel than piston engines do. Where do you cram all that fuel? That could lead to more serious CG issues as well...
Hence, why Republic chose to design the P-84 Thunderjet from scratch rather than do some lash up converting an existing design into a jet like the Russians chose to do early on.
If, as the narrative given, the J35 axial turbojet is used instead of a J31, then the whole exercise is a waste of time. The J35 wasn't available prior to WW 2 ending and post war there is no rush involved in getting a jet fighter into service. The USAF would have no reason to want to make some sort of lash up, half-solution out of an older piston engine fighter over designing a proper and clean design from scratch, especially when they already had these well advanced in 1945. Totally fake.