If you are online and do not respond to a message it goes as 'Missed Conversation...' to your Inbox
But if you are offline, Lync can not take the message from the other party and says the recipient is offline.The Lync should take the message and send to us as 'Message recieved when Offline' right?
Was this intentionally or inadvertently left by Lync team?
In websites' which provide live chat/support, they provide this feature too. When you are offline
it collates the messages and sends you through email.