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Thank you for sharing your concern.
Unfortunately, this behavior is expected by design in Exchange Online. A shared mailbox can only send or reply using addresses that exist within your tenant, such as its own address or configured aliases. It is not possible to send or reply using an external address, such as a personal Outlook.com account or any account that is not hosted or managed within your Microsoft 365 environment.
You can refer via:
Manage permissions for recipients in Exchange Online
In your scenario, although emails are successfully forwarded from the Outlook.com account to the shared mailbox, the original Outlook.com address remains an external identity. When users reply from the shared mailbox, Exchange Online requires the “From” address to be a valid mailbox or alias within the tenant, so it cannot send as the external Outlook.com address.
As a best practice, you may consider using the shared mailbox address as the primary communication address for replies, which aligns with the intended design of shared mailboxes. If retaining the Outlook.com account is required, replies would need to be sent directly from that account rather than through the shared mailbox.
I hope this helps.
Please feel free to correct me if I misunderstood your request. If you have any additional concerns, feel free to comment below. I would be more than happy to assist.
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