If your have issues using the message trace in O365 to download the report, you can use the following syntax in PowerShell:
Start-HistoricalSearch -ReportTitle "Search" –RecipientAddress [email protected] –SenderAddress [email protected] -StartDate mm/dd/yyyy -EndDate mm/dd/yyyy -ReportType MessageTraceDetail -NotifyAddress <email address of a user of domain where you want to receive the notification>