If it is the same one I have in mind, they also played the "Inno di Mameli", a song that, despite being rather popular also in the first half of last century, became the Italian national Anthem only in 1946, until I wrote them complaining about the gross historical inaccuracy.
Never mind, I have more than 400 songs of WW2 era, most of them from Italy and Germany ( ca 100 from each Country), but also Soviet, Americans,Spanish, British, French and Polish, I would be glad to share them, but I don't know about copyright issues ( I downloaded all of them from websites that offer them for free, so I suppose they have the right to do so and that I have the right to share them, but I cannot offer any guarantee) and I don't know how to upload.
Also, I am not aware if some of them are illegal in Germany or other Countries.