After studying the pages found on the Internet, I conclude that Portable Timekeeper doesn't have a feature to communicate through the Internet, therefore impossible to send the data.
Here is a simple solution if the software saves the data to files locally. Install Google Drive or Dropbox and a folder to synchronize online, then install the same app on the other PC and choose the folder as a ONE-way sync. That way, when you add files from the 1st PC, it will automatically be synced on 2nd PC.