Like all of Europa, Germany and Italy have thousands of years of history together. You are using nationalist terminology that is not even 200 years old to try t

Like all of Europa, Germany and Italy have thousands of years of history together. You are using nationalist terminology that is not even 200 years old to try to grasp 2000 years of history. At the time king Ludwig I of Bavaria acquired that bust, the nation you identify as "Italy" didn't yet exist. And that was in the early modern. For most of the medieval age, the small territories that today are within southern germany and northern italy were vassals of the same empires. And while europa sure was almost constantly at war with itself, there was also a lot of trade going on. Who took that bust from whom and if they paid with coin or sword is most likely lost to time.