You can set up your Edelweiss account so that you can submit reviews from Edelweiss to Goodreads. The reviews and ratings will appear on Goodreads. Updates/Edits to reviews in Edelweiss will reflect in Goodreads (although updates on Goodreads will not appear in Edelweiss).
Click Request for a DRC:
Click on it, and you’ll be taken to Goodreads. You’ll need to log in, if you’re not already, of course.
Once you allow access, you’ll see that you can now submit a review to Goodreads when you submit your reviews.