A quick look at the parts catalogue sheet on Cousins suggests that your spring isn’t quite the right shape which will always make the guesswork harder. Cousins has them in stock at only £2.20 so worth getting a replacement.
The installation is a little unusual, but the Google drive link in this thread has a pretty good image
https://www.watchrepairtalk.com/topic/1919-favre-leuba-253-service/page/2/
There is also a suggestion in that thread that the barrel arbours might not both be the same. Worth a check they are in the right places.