First off it's worth noting that Inbox messages can be controlled with rules. Outlook.com / Outlook Web App (OWA) is intended for those on the go. Email can be accessed from anywhere. The account can be connected to some of your favorite apps such as Skype. It does however have limited features. The OWA is a "compact" edition of sorts. Rule settings only apply to the Inbox. Retention policy settings (OWA for business) appear to reflect the Inbox only as well. Therefore rules cannot be specified to the Sent Items folder in OWA currently.
If you have Outlook 2013/2016 (not OWA), there are more features to help you manage your account settings. In Outlook 2013/2016, you would not need to create a rule that deletes messages from the sent folder. There is an option to not save sent messages at all. After you connect your email account in Outlook 2013/2016. The following steps can used for this option.
*Please note that there is also an option to save sent messages. Then archive/delete them after a time frame of your choosing. The following steps do not include this option.*
1. Go to File>Options
2. Select Mail from the left column.
3. Scroll to "Save Messages"
4. Deselect the box "Save copies of messages in the Sent Items folder"
5. Click OK
You should never see a message in the Sent Items folder for this mailbox afterwards. Repeat the steps for other mailboxes where applicable.
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