At the end of the night you can FTP or MAIL the log file to your personal account at your home institute. You can also print a copy. Use the PRINT menu button on the logger window, to print a log or to write it to a file.
After writing the log to a file, you can email yourself the log file with
SYS> Mail -s 'subject-text' email@example.com < 'logfile-name'