I have checked your website and I can see you have Object cache enabled, it can sometimes cause issues. Can you please disable it and then check again?
Also, I would advise updating to the latest WPML as it brings some improvements to this process.
Go to Plugins > Add New > Commercial > Click “Check for updated" and update WPML plugins to latest versions.
Please make sure to create a backup, before doing any actions, just in case.
The field groups post type was set to be translatable, while it shouldn't be translated, so I changed its translation preference. (Kindly check this hidden link">screenshot)
After that, I opened the translation editor, which worked as expected. (Kindly check this hidden link">screenshot)