Depending on how your organization has set up Lync 2013, you may be able to save and retrieve your old instant messages. Watch this short video to help you learn whether you have that option and, if so, how to change the setting.
Then, if you want more details, see the Help article Find a previous Lync conversation.
Other videos in this course
This video is part of a training course called Set up Lync for Office 365.