It looks like that the problem there is with the permalinks, they are missing the ‘/en/’ part for some reason. By default the plugin searches only the currently active language. The items I see are translated, but the link is not completely correct, which is odd, because it’s requested from WPML directly.
Anyways, I beleieve this could be possible to fix with a small custom code snippet easily.
Add this custom code to the functions.php in your theme/child theme directory (copy from line 3 only!). Before editing, please make sure to have a full site back-up just in case!
If you need any help with this, just add temporary FTP details to your ticket, and I will add this code for you.Best,
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