How to export conversation history from Microsoft Communicator for Mac (2011)?
After running this command, 

find ~ -type f -exec grep "special search string" {} \; -print


I was able to find the Conversation history at

/Users/&lt;my_mac_user_id&gt;/Documents/Microsoft User Data/Microsoft Communicator History/&lt;my_communicator_login_id&gt;


Just copying the entire folder to new mac solved my problem.

"special search string" is an unique string you would have used while chatting with your friends/colleagues.