Note: in Skype for Business 2016, there is no option to select Microsoft Exchange or Microsoft Outlook, instead it would say Note: Intergration is controlled by your admin.
On the Personal tab, choose Microsoft Exchange or Microsoft Outlook from drop-down menu and select Save my IM conversations in my email Conversation History folder.Click Show Menu arrow next to the gear icon in the top right and select Tools > Options > Personal.
Note: Though the interface differs in Skype for Business, Lync 2013 and Lync 2010, the steps to enable this feature are the same for all applications. To turn on the option for storing chat history: Read this article for more information What Is An Autodiscover Record And Why Do I Need It? Note: Make sure that your domain has a valid autodiscover record. This option is only supported if you are using Outlook as the Default mail client. You can store copies of your Skype for Business/Lync chat conversations in your Outlook to refer to later.
