Sending, receiving, and organizing email in Outlook.com
I assume you've already checked the Online Archive. If you're unable to locate the email there or complete mailbox, the next option would be to perform a Content Search for the required date range. Any emails that still exist in the mailbox and are searchable will be returned in the results. Once the search is completed, you can review and export the matching emails as needed.
If you need assistance, you can raise case with Microsoft Purview support or Microsoft Exchange Online support.