Hi,@StefanoC
Thanks for posting your question in the Microsoft Q&A forum.
The on-premises one will have to configure federation. Federation refers to the underlying trust infrastructure that supports federated sharing, which is an easy way for users to share calendar information with recipients in other external federated organizations.
You can refer to this link:https://learn.microsoft.com/en-us/exchange/configure-a-federation-trust-exchange-2013-help?source=recommendations
After completing the federated authentication trust, you need to configure the organizational relationship between the two organizations:
You can refer to this link:https://learn.microsoft.com/en-us/exchange/sharing/organization-relationships/organization-relationships
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.