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Considering your concerns, here are some other methods for your reference:
- By manually adding a shared mailbox account to Outlook, please follow these steps: Open the Outlook client, select File --> Add Account, on the "Automatic Account Setup" screen. Enter the email address of the shared mailbox, for the password, please enter the password for your own email account. Then select Next to proceed. Change the email address to sign in with by selecting Sign in with another account. Sign in with your own account credentials and select Finish. You will need to restart Outlook for the changes to take effect. After restart Oulook. Click Rules --> Manage Rules and Alerts to edit.
- Run the following cmdlet in Exchange Online PowerShell: Set-MailboxAutoReplyConfiguration
- Try to sign in to the Microsoft 365 portal, then locate Groups > Shared Mailboxes, select a user who has a Microsoft Exchange mailbox, and find Automatic replies on the flyout on the right.
Additionally, for more information, you could refer to: How to set automatic replies on a user's mailbox in Microsoft 365 - Exchange | Microsoft Learn
Add rules to a shared mailbox - Microsoft Support
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