The orange Miura in question here is #3586, and is verified as the one driven by actor Rossano Brazzi (playing Roger Beckermann in the film) and stunt driver Enzo Moruzzi on the Great St Bernard Pass. We'll put the video right here for you, since those who haven't seen it need to, and those who have most certainly want to watch it again now.
Lamborghini's in-house restoration unit, Polo Storico, did all the work to certify and restore the Miura. It's been a long-time coming, too — this Miura has been off the map since the filming ended and Lamborghini sold the film car to someone in Italy. The car was found in The Kaiser Collection of Vaduz, which happens to be in Liechtenstein. Lamborghini is certain this is the right one after looking at the documentation, company archives and a full examination of the car itself. Testimonials from enthusiasts and former Lamborghini employees further solidified the belief that this was the movie car.
The only difference you'll notice between this fully restored Miura and the movie scene is the color of the seats. Lamborghini swapped out the white seats for black ones, as they were worried the white seats wouldn't make it back to the factory in perfect condition. However, there was no time to swap the headrests (mounted to the dividing glass) for black ones to match the seats, which you'll notice in the movie scene.
We know we'll have "On Days Like These" running through our heads for the rest of the day on account of this incredible find. Thankfully, Lamborghini provided a bunch of photos to look at the car post-restoration, so go check them all out above as you race to your VCRs to watch the film once more.