You can set up your Edelweiss account so that you can submit reviews from Edelweiss to Goodreads. The reviews and ratings will appear in Goodreads. Updates/Edits to reviews in Edelweiss will reflect in Goodreads (although updates in 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. Once you’re logged in to Goodreads, access authorization happens automatically. When completed, you’ll see that you can now submit a review to Goodreads when you submit your reviews in Edelweiss.