Hi Jeffroe,
Can these sent messages be searched in Outlook client? If you can find these messages, just hover your mouse over the message and it will show the folder where the message is located.
Besides, please check if you have ticked the box of "Save copies of messages in the Sent Items folder".(File > Options > Mail)

For your reference: Change where sent email messages are saved.
Hope this can be helpful.
Regards,
Aidan Wang
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