Send As Exchange Online Mailbox in Hybrid Exchange

Question

We have an Exchange Hybrid model with most of the mailboxes on-premises and all accounts in local AD, synced to Azure via AADSync.
Now I do have two mailboxes online and want to grant other users (local AD and local mailbox) Send As privilege on these mailboxes.
This does work for me, but I am also some super administrator, at least i have several powerful admin roles, but it does not work for my regular users in charge.
I have granted mailbox delegation for "Read and manage" + "Send As" (not send on behalf), but every time they try to send out emails from their Outlook the get the message that they are not allowed to send on behalf of that recipient.
First of all, they shouldn't send on behalf (if I'd grant that permission that would work), but send as, and second are they missing some special role or something? Because, as I said, for me it works, for them, it doesn't.

I have also checked permission on the mailbox, it is about user Michaela, see attachment.

This is a different screenshot, on another mailbox there is another user with same permissions, plus myself, how I am the only one which can send as.

Any idea? I have granted these permissions about 4 hours ago.

Answer 1

Try this:

Get-RemoteMailbox xxx@company.de | Add-ADPermission  -User michaela.yyyy-zzz@company.de -AccessRights ExtendedRight -ExtendedRights "Send As"

Answer 2

OK, I think I got you now, but the problem is that if I try this, it tell's me that the o365 user (mailbox) isn't fond on my local DC, not even to show permissoins

Get-MailboxPermission -Identity "mobilexnew\xxx" | Format-List
The operation couldn't be performed because object 'mobilexnew\xxx' couldn't be found on 'dc2-2019.xxx.intra'.

or

Add-ADPermission -Identity xxx@company.de -User michaela.yyyy-zzz@company.de -AccessRights ExtendedRight -ExtendedRights "Send As"
xxx@company.de wasn't found. Please make sure you've typed it correctly.

So, it looks like I cannot get or grant Send As permission to an AD user which mailbox is remote, online. Eventually if I do manually set the respective attribute in AD, but I have no clue which one it might be.