You're not going to get the body of messages with any PowerShell command since that's not saved anywhere. If you have subject logging enabled for message tracking, you can get the subjects. For that, you could look at Microsoft's free Log Parser tool or the third-party Quest MessageStats, which has canned reports that might just meet your needs.
Hi,
I recommend you use the following cmdlet to enable Message Tracking Log Subject at first.
Set-TransportServer cashub01.nourd.com -MessageTrackingLogSubjectLoggingEnabled $true
And then use the cmdlet below to export the message subject to a csv file. As Ed said, I'm afraid that there is no built-in feature to export the message body.
Get-MessageTrackingLog -Recipients "user@domain.com" | Export-Csv c:\test.csv
Hope it helps.
Best regards,