It looks like this is painful and per language, no simply just copy all the translations over. It looks like the process is different for strings and posts/pages too?
Resources
https://wpml.org/forums/topic/transfer-my-translations-from-one-to-another-website/
Feel free to comment if you can add help to this page or point out issues and solutions you have found. I do not provide support on this site, if you need help with a problem head over to stack overflow.