Send-AS Permission in On-Premise Exchange environment can be assigned using the below PowerShell command,
Add-ADPermission -Identity “UserAccount” -User “UserwhoNeedsPermission” -AccessRights ExtendedRight -ExtendedRights “Send As”
But, as per Microsoft article, Send-As Permission over cross Exchange platform like Hybrid Exchange environment is not supportable. But still, you can run the below command to provide Send-As Permission for a On-Premise Mailbox on a Mailbox in Office 365.
Add-RecipientPermission “UserMailbox” -AccessRights sendas -Trustee “On-Premise Mailbox”