This thread is resolved. Here is a description of the problem and solution.
Problem: Only the wp-admin folder is hosted on a different subdomain. WPML doesn't recognize this and send calls to file which aren't on this subdomain
Solution: you need to edit the \wp-content\plugins\sitepress-multilingual-cms\classes\language-switcher\class-wpml-ls-assets.php file (see Relevant Documentation)
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