Dear @Dr.aka,
It depends what nationality he has. If he is from one of these countries, he can apply for a residence permit to study while he’s here in Germany:
Australia, Japan, Israel, Canada, South Korea, New Zealand, UK, Andorra, Brazil, El Salvador, Honduras, Monaco, San Marino.
If he has a different nationality, he must apply for a visa to study in Germany at a German embassy. If he has a permit for Italy, he can apply with the German embassy in Rome. He will have to show he has been accepted to a German university and that he can support himself financially.
Here’s the information from the German embassy in Rome (in German) about the required documents:
https://italien.diplo.de/blob/1457244/4614a003f345b90c0045978db165e830/visa-studium-data.pdf
Best,
Éanna