Outlook 2013 and Outlook 2016 for Windows uses Exchange ActiveSync (EAS) to connect to Outlook.com (formerly Hotmail), which doesn’t save sent messages in the folder you sent them from. Instead, Outlook stores them in your Sent Items folder.
If you have a mail account that isn’t an Outlook.com account or another Exchange ActiveSync account, use the steps below to save your sent messages in the originating folder.
In Outlook, click File > Options > Mail.
In the right pane, under Save Messages, check the When replying to a message that is not in the Inbox, save the reply in the same folder box, and click OK.