Scenario: you want to forward emails that comes to a particular mailbox to an external address and also keep the mail.
Resolution: Create a mail contact using powershell or Exchange 2013 ECP. If you have exchange 2010 users, you can also use the mgmt console
From Powershell, type Set-Mailbox -Identity ‘testmailbox’ -DeliverToMailboxAndForward:$true -ForwardingAddress ‘mailcontactalias’
Ex-Shell 