According to the seller, this car was built by S.I.A.V. (or better, in its building) in 1950 from a '36 Fiat 500a.
The car is now completely restored but oddly enough, when I asked the owner if the car was the same of the previous year, (when I saw it for sale in his stand and was in the puzzle car's configuration) he said it was not!
This is the car today:
(I saw the papers the seller has got, but there's nothing about this very car but some letters)