You cannot migrate mailbox off of Office365 while the mailbox has a connected account enabled

Exchange hybrid is the only Microsoft migration method that allows you to move mailboxes in both directions between Exchange and Office 365.

I'm working with a customer who is offboarding their mailboxes from Exchange Online back to Exchange Server 2016. Several mailboxes cannot be migrated back to on-premises due to the following error:

You cannot migrate mailbox '2f15ec3c-b024-4a25-2fdf-bfda9fd806ba' off of Office365 while the mailbox has a connected account enabled. To successfully remove the connected accounts, run the following command: 'Get-Subscription -Mailbox MailboxID -Aggregati

Note the truncated command, which isn't very useful. 

The Get-Subscription cmdlet let's you view the properties of an existing subscription configured in a user's cloud-based mailbox. This cmdlet is used by Outlook on the web Options to display the list of email subscriptions that the end user has, such as POP, IMAP, Facebook, and LinkedIn.

The exact issue with the mailbox can be determined by running the following in Exchange Online PowerShell:

Get-Subscription -Mailbox user -AggregationType all | select DisplayName, Name, AggregationType, UserId, LastModifiedTime, LastSuccessfulSync, CreationType, Status, StatusDescription, DetailedStatus

We can see that the user has configured a subscription to LinkedIn so that Outlook can do a PeopleConnection lookup. This service was closed down by Microsoft over 3 years ago, but the subscription on the mailbox remains.

Run the following cmdlet in EXOPS to remove the subscription from the mailbox:

Get-Subscription -Mailbox UserId -AggregationType All | Remove-Subscription

Now you can resume the mailbox migration to complete the offboard.