This is a very well know issue or you can say not well known for most of the admins

The issue is the auto mapping option

This option

Auto-mapping is an Exchange on-prem & Exchange Online feature, which automatically opens mailboxes with Full Access permissions in a delegate’s Outlook client. The setting is configurable by an Administrator when Full Access permissions are assigned to a user. Once enabled, the periodic Autodiscover requests from the Outlook client will determine which mailboxes should be mapped for a user.

This is the automapping

When you delegate a user permission on a shared mailbox it must appear in the outlook by default you can disable it by PowerShell but it’s enabled by default

The scenario is that a hybrid users (users who have been moved to online exchange in the hybrid environment) will have two problems

The problem

When a user mailbox was on the on-prem exchange and the mailbox had a delegation on the shared mailbox then the mailbox has been moved to online exchange you will face two problems

1. The delegation isn’t working anymore cause simply if you try to give delegation to the remote mailbox on the on-prem shared mailbox the user will not be found
2. Another problem is the automapping option will now work and this is related to the Auto Discover option

Solution

Move the shared mailbox online and then make sure that the default reply address is the

sharedmailboxname@yourdomain.onmicrosoft.com

Then wait it will be synced and appeared in your outlook

It will take a while

Or you can just create

new shared mailbox on the exchange with default the choose this domain

sharedmailboxname@yourdomain.onmicrosoft.com

Or you can just log in through your OWA

How to remove auto mapping in shared mailbox

https://support.microsoft.com/en-us/help/2646504/how-to-remove-automapping-for-a-shared-mailbox-in-office-365

ref: https://support.microsoft.com/en-in/help/3129334/users-in-a-hybrid-deployment-can-t-access-a-shared-mailbox-that-was-cr