So you're an Office 365 administrator and you've granted yourself, or someone else, "Full Access Permissions" to another user's mailbox — either in Exchange Management Console or in Exchange Admin Center in the Office 365 Portal. You did this because you needed to access the user's mailbox to receive something or work on an issue. You're done working on that issue and no longer want that user's mailbox attached to your personal Outlook account. You're used to simply "Closing" the folder on the left navigation menu and/or removing/adding the mailboxes via File > Account Settings > Account Settings > opening your account > More settings… > Advanced > Additional Mailboxes. However, you do that like you did when Exchange was on-premise, but that's no longer working with Office 365. You get the following message:
This group of folders is associated with an email account. To remove the account, click the File Tab, and on the Info tab, click Account Settings. Select the e-mail account, and then click Remove.
The issue is most likely that Office 365 + Outlook has a feature called "Auto Mapping" — Autodiscover automatically maps to any mailbox for which a user has full access permissions. If a user is granted Full Access permissions to another user's mailbox or to a shared mailbox, Outlook automatically loads all mailboxes to which the user has full access. This feature was available in Exchange 2010 SP2 and Outlook 2010+, I believe, but in my experience it wasn't as intrusive as it seems to be when you introduce Office 365/Exchange Online into the mix.
This creates a conflict/confusion with Outlook when you want to remove the Shared user mailbox.
In the Exchange Admin Center in the Office 365 Portal, remove "Full Access Permission" from the user's mailbox.
Then, you're going to grant Full Access BACK to the user, via PowerShell, while passing the command to NOT AutoMap. Doing this should then automatically remove the attached mailbox(es) from Outlook.
Run PowerShell as an Administrator, and enter the following commands:
$UserCredential = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/ -Credential $UserCredential -Authentication Basic -AllowRedirection
*Wait 3 minutes*
Add-MailboxPermission -Identity emailaddressofuseryouwanttoremove -user emailaddressofuseryouwantmailboxremovedfrom –AccessRights FullAccess -Automapping $false
In about 30 minutes, you'll see the attached mailbox(es) automatically disappear from Outlook.