Generally speaking no, as this is admin-level operation. That said, the user might obviously notice any changes made to items within the mailbox or its configuration. And obviously there might be some legal implications.
User Mailbox Permissions

Hello,
using the MS365 Exchange Admin interface I grant full permissions on a user's (A) mailbox to another user (B).
My question is simple: is user A able to find out that user B has access to his mailbox?
Thank you,
Andrea
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2 additional answers
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Andrea Cavenago 21 Reputation points
2020-12-16T13:40:00.903+00:00 Thank you for your answer michev!
Do you know if the mailbox will automatically pop-up in Outlook of user B or needs to be opened? Outlook is at its latest version (16.0....).Andrea Cavenago 21 Reputation points2020-12-21T16:25:00.807+00:00 Thank you both!
I used the following script because I need it to not auto-appear in Outlook:Add-MailboxPermission -Identity user1_mailbox -User user2_mailbox -AccessRights FullAccess -AutoMapping:$false
Thanks again,
Andrea
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@Andrea Cavenago
Agree with michev. Just add more information, if you grant Full Access permission from EAC or M365 Admin center, the mailbox will auto appear in the Outlook by default. Additionally, we have to wait for a while before test to make sure the permission takes effect.
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