Hi ClannadYoung1854-8750,
I’m afraid that this feature is not supported now.
Every time when you start a new conversation, you can only delete this part of conversation separately. The prerequisite is to uncheck an option (Options > Personal > Save IM conversation in my email Conversation History folder) to disable any conversation generated in the Conversation History folder in Outlook. After doing that, when you manually delete the conversation in Skype for Business, the same conversation won’t generate in Outlook anymore.
We recommend you that please give a feedback to https://www.skypefeedback.com/forums/299913-generally-available/suggestions/41245561-delete-the-conversation-for-specific-user-in-sfb.
Microsoft will always focus on customer’s feedback and experience. Some new features would be added to the services based on customers' feedback in the future, and your good ideas will be very helpful for them to improve the service.
Your time, understanding and cooperation will be highly appreciated.
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