Stat/Transfer always writes a log that is displayed in the Log dialog box. You can view it and, if you would like, manually save it to disk.
However, you can tell Stat/Transfer to automatically write a log file to disk every time you do a data transfer. The log file will contain detailed information about what has occurred during your transfer.
To turn on this feature, check the option, Automatically write a log file in the Transfer Logging/Statistics section of the Options dialog box.
By default the log file will go to the same directory as your output file and will be appended to an existing log file. Options in the Transfer Logging/Statistics section allow you can change the name and whether or not an existing file is overwritten.