Conversations in Skype For Business will be archived in Outlook's Conversation History on your workstation or in Outlook on your mobile device once the conversation thread goes idle. Conversations will remain in the Conversation History folder for a maximum of 3 days
Remember: The Conversation History folder in the Outlook email inbox on your workstation is reserved for retaining Skype for Business Instant Message (IM) conversations only. DO NOT use this folder to store emails because the contents are deleted after three days. If you wish to create a new folder in which to store and retain email messages, refer to the guide Creating a New Folder for Saving Emails.
If you miss an IM conversation, Outlook will generate an email to notify you. The notification feature is by design so that the SfB mobile app can interact with the SfB client on one’s workstation. It cannot be disabled. What users can do is create a rule in Outlook to move the emails with “Missed conversation….” in the subject line to the Deleted Items folder. See this tip sheet on Creating a Rule in Outlook for Missed Conversation Messages.