This script help you to add permission (full & sand as) an a shared mailbox in a hybrid exchange configuration.
type this command in you exchange online PS
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$SharedMailbox = “sharedmailbox@i-ricci.com”
$UserAccount = “usermailbox@i-ricci.com”
#remove full access permissions for the affected user from the shared mailbox
Remove-MailboxPermission $SharedMailbox -User $UserAccount -AccessRights FullAccess
## Add Full Access permissions back on, but make sure you set AutoMapping to FALSE!
Add-MailboxPermission $SharedMailbox -User $UserAccount -AccessRights FullAccess -InheritanceType all -verbose ### -AutoMapping $false
Add-RecipientPermission $SharedMailbox -AccessRights SendAs -Trustee $UserAccount
## shared mailbox
Get-Mailbox $SharedMailbox | Set-Mailbox -MessageCopyForSentAsEnabled $True