We don't, however, support the use of the Send-As, Receive-As, or Send on behalf of mailbox permissions in hybrid deployments ...

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 %BRAND_EXCHANGE_ONLINE_SHORT% and %BRAND_OFFICE_365_SHORT% 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 %BRAND_EXCHANGE_ONLINE_SHORT% and %BRAND_OFFICE_365_SHORT% organizations. Learn more at Permissions in %BRAND_EXCHANGE_ONLINE_SHORT% hybrid deployments.