Is there a trace of POPcon's actions somewhere so we can check where email messages came from and where they went?

Yes, POPcon's actions are logged in the POPcon logfile POPconSrv.log in the c:\program files (y86)\POPcon folder.

You can read this log file with any text editor like notepad.

POPcon cuts down the size of the log file once a day to the value set on the GENERAL configuration page, removing older entries first. You can extend the length of the log file or even switch to individual daily log files without size restrictions on the GENERAL configuration page in the POPcon configuration.