You can save the log file at any time by just making sure that it's the current active window by clicking on it, and then clicking on File | Save As. The default name is "log.jsl", but obviously you can change that to anything you want, after which you can pick it up in WordPad, MS Word or whatever.
If you want to preserve the colour-coding of the text as well, just copy the contents of the log onto the clipboard with -A, then paste it into Word or WordPad with either an Edit | Paste or -V in the usual way.