Hello, @Stefano Colombo,
Welcome to the Microsoft Q&A platform!
Yes, to ensure that users with mailboxes on Exchange Online can see the contacts in their Global Address List (GAL), you need to sync those contact objects from your on-premises Active Directory (AD) to Entra ID. This synchronization will make the contacts available in the GAL for both on-premises and Exchange Online users.
For more information, please click on https://learn.microsoft.com/en-us/entra/identity/hybrid/connect/concept-azure-ad-connect-sync-user-and-contacts for reference.
The same applies to distribution groups. If you want users on Exchange Online to see and use the distribution groups defined in your on-premises Active Directory, you need to synchronize these groups with Microsoft Entra ID as well. This ensures that all users, regardless of where their mailbox is hosted, have access to the same GAL.
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Thank you for your support and understanding.
Best Wishes,
Alex Zhang