Support for cross-premises mailbox permissions

Exchange hybrid deployments NOW support the use of the Full Access mailbox permission between mailboxes located in an on-premises Exchange organization and mailboxes located in Office 365. A mailbox on an on-premises Exchange server can be granted the Full Access permission to an Office 365 mailbox, and vice versa. For example, an Office 365 mailbox can be granted the Full Access permission to an on-premises shared mailbox.

We don’t, however, support the use of the Send-As, Receive-As, or Send on behalf of mailbox permissions in hybrid deployments between on-premises Exchange and Office 365 organizations. These permissions are only available when both the mailbox granting the permissions, and the mailbox receiving the permissions, are in the same organization. Any mailboxes that receive these permissions from another mailbox need to be moved at the same time as that mailbox. If a mailbox receives permissions from multiple mailboxes, that mailbox, and all of the mailboxes granting permissions to it, need to be moved at the same time. In addition to these permissions, the Auto Mapping feature is also unsupported when used between mailboxes in the on-premises Exchange and Office 365 organizations.

Source:
Exchange Server Hybrid Deployments
https://technet.microsoft.com/en-us/library/jj200581%28v=exchg.150%29.aspx