I am not sure you will be able to just move the application from your old PC to the other PC. Since it was part of Microsoft Office (97 I think), you might have to install the same Office suite on the other PC. The application itself is likely stored in one of the Microsoft Office folders. I "googled" it, and there are a few sites that offer downloads, but they all look sketchy. Not sure why, but Microsoft decided to abandon the application a while back.

If I may ask, are you just wanting to move it to the other pc to do basic editing? If that is the case, there are several other basic photo editors that are free for Windows.

On Windows 7, you can right click on a photo and select edit. That will give somewhat similar options as Photo Editor did.

Here is a link that might help: http://www.sevenforums.com/music-pictures-video/221827-i-want-my-ms-photo-editor-back.html

Though I will mention that I haven't tried it, and can't promise that it will work without issues. One person on that forum mentions they are getting registry errors, likely cause by not having all the files that would be found in the full Office Suite install.

Hope this helps!