Office 365: How to edit Exchange stuff in 365 when synced from local AD?

My boss migrated our Exchange server to 365 last week. Then he quit the company (technically I'm going to see him one more day next weekend but I doubt he'll be able to fix this in the time we have).

Now, when I need to add Full Access or Send As permissions for a mailbox in 365 Admin, I get this error:

The operation on mailbox "IT Vendor" failed because it's out of the current user's write scope. The action 'Set-Mailbox', 'EmailAddresses', can't be performed on the object 'IT Vendor' because the object is being synchronized from your on-premises organization. This action should be performed on the object in your on-premises organization.

Some Googling around leads me to believe that because our local AD is still the "Source of Authority", I won't be able to make changes like this from the 365 Admin panel. This blows.

So it looks like...