Hi Jean-Claude,
There's no need to copy the application or anything from ~/Library. Just install it from the App Store on both machines. In the App Store application on your 2nd Mac, using the same Apple ID you used for the purchase on your 1st Mac, click on Store ▸ View My Account and then click the download button. That way it also gets automatically updated when needed on your 2nd Mac.
To share the images & Observatory libraries, put them both on that external SSD. I have never tried this myself, but as long as you always save and close the library on one computer before opening it on the other it should work. It is likely that sandbox permissions will get in the way though, making it necessary for you to help Observatory to locate the source folders when you switch between the computers. That is currently not recursive (the fix for that is targeted for the next release).
Let me know if you run into issues.