You have a hybrid Exchange environment and you need to grant SendAs permissions for a user on a mailbox.
The location of the mailbox matters here as the commands differ depending on whether the mailbox is in the cloud or on-premises.
You must have the correct Exchange role permissions to apply mailbox permissions.
Important. You must have the Exchange role access that allows this.
Add-RecipientPermission ` -Identity "Fakey Shared Mailbox" ` -Trustee "Fakey McFakerson" ` -AccessRights SendAs
Add-ADPermission ` -Identity "Fakey Shared Mailbox" ` -User "Fakey McFakerson" ` -ExtendedRights Send-As