The way that send as /send on behalf of permissions work has changed since we upgraded to Exchange 2013 ( Office 365)
If someone has 'send on behalf of' permissions to another persons mailbox ( e.g if Debs Spendlove had send on behalf of Permissions to Joe Bloggs' mailbox)
They will be able to send emails that say
'sent by Debs Spendlove on behalf of Joe Bloggs'
but won't actually be able to send emails that say
'sent by Joe Bloggs' - to do this they need would need the 'send as' permission
To Send on Behalf of
go to the 'From' drop down list and select
'Other email address...'
Then search for person's email address in the From box
and select your own email in the 'Send Using' drop down