Discussion:
Various web sites indicate the car was either just by Figoni, or by Figoni & Falaschi. The almost-triangular badge near the lower front of the door in the B&W image, resembles that of Figoni & Falaschi. A similar badge appears on the puzzle car image, near the top door hinge. This badge is not present on many of the modern, color images of this car.
Various publications call this car Amilcar Racer, Amilcar Grand Prix, and "competition voiture".
There are some obvious differences between the puzzle car and the B&W image. The puzzle car has external door hinges, and the doors open from the rear. The B&W car has completely hidden door hinges, so we cannot tell if they open from the front or the rear.
The central windshield/screen split is much thinner/more delicate on the B&W car.
The width of the cowl area between the door and the hood/bonnet, is narrower on the B&W car. An F&F badge would not have fit in that location on the B&W car.
The tie down locations for the top of the B&W car, are entirely on the bodywork of the car. The puzzle car has these items in a different line, on both the body and tonneau cover.
Many of these differences could be production variances for a very-low production hand-built vehicle. But they could also indicate the puzzle car is a more modern interpretation of the original.
Seeing the B&W image, the wire wheels on the puzzle car start to look too modern/large.