The conversation history is saved in Outlook and viewable from the client but you cant see the chat history when you open a chatwindow with a user.
It would be good to see the last conversations and last Contact when you start to chat with a user.
The feature was included in Live Messenger and very useful.
So, I am on my computer. My conversations are saved. Then I needed to leave but kept my conversation going on my phone. I believe that after the conversation, in the settings of Lync Mobile, I should be able to choose which Email address represent my work Email so that all conversations from it is sent to my inbox which could then be ruled into my conversation history folder.