My helpdesk is a member of the Exchange Recipients Management group in AD and previously had access to manage Send-As in Exchange 2007. After being migrated to Exchange 2013, they no longer see the SendAs + symbol but can manage Send of Behalf of and Full Mailbox access.
Anyone run into this. I see from this article, that Recipient Management should give them the rights.
https://technet.microsoft.com/en-us/library/dd638132(v=exchg.150).aspx