Hi, @Roger Roger
In Exchange 2016 hybrid environment, providing delegated or calendar access to shared mailboxes for guest users can be somewhat complex because of certain limitations and constraints.
First, delegated permissions across environments are migrated via DirSync, but delegated access may not work properly when principals and delegates are distributed across on-premises and online environments. This means that if the shared mailbox is in Exchange Online and the guest user is on-premises, or vice versa, delegated access won't work as expected.
In addition, mailbox permissions, such as Send As and full access, are migrated when a mailbox is moved through the Mailbox Replication Service. However, the mailbox permissions for referenced distribution lists and mail-enabled users are not retained and must be manually re-added using cmdlets such as Add-RecipientPermission and Add-MailboxPermission.
If you've created a mail-enabled security group and added guest users, you need to make sure that these guest users have the appropriate licenses and are properly configured in Azure AD, make sure that mail is enabled, and sync between on-premises and Azure AD, then you can try the following commands.
If you want to assign full access:
Add-MailboxPermission -Identity smb@contoso.com -User YourSecurityGroup@contoso.com -AccessRights FullAccess -InheritanceType all
If you want to assign calendar access:
Add-MailboxFolderPermission -Identity smb@contoso.com:\Calendar -User YourSecurityGroup@contoso.com -AccessRights Editor
More information can be found Add-MailboxFolderPermission (ExchangePowerShell) | Microsoft Learn
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