For one who is determined to be stupid, it is impossible to acquire an education through the efforts of others.
Italians do not claim to be the Roman Empire, because the Roman Empire was not a single, undivided mass. If you open a textbook of Roman history (you might have noticed that I use this phrase a lot when responding to your mails; ever wonder why?), you will find that the Roman Empire was one thing, Italia was another. It was only Italy that Italians claimed, not Rome, not the Roman Empire, but Italy.
In the days of city-states, that preceded mediaeval personal realms, that in turn preceded Westphalian nation-states, it was never a country, never a region that became an empire. It was a personal realm, as in the case of the Achaemenids, arguably the first empire in the world, or in the case of the Macedonian Alexander III, or it was a city, as in the case of Carthage, or in the case of Rome. So there was no question of a nation-state of Westphalian type equating itself to an empire such as the Roman.
The modern Italy is almost exactly the area occupied by the area known as Italia under the Roman Empire. Modern Italians are almost exactly the same as ancient residents of Italia, except for the Lombard (Langobard) element north of the Po, and the very mixed elements, including Greek, Arab and Norman, on top of a solid Italian sub-stratum, in Sicily.
I wish you would stop labouring this point until you had educated yourself further. It makes dismal reading.