WPML Translation of custom emails

I am having trouble translating the custom emails that the plugin Theme My Login is sending.
I have included the appropriate fields in the WPML-config.xml file and the strings are read from the wp-options table. They appear in the string translator and I have translated them, subject and body as well. They appear under the domain “admin_texts_theme_my_login_email”, for example with the name [theme_my_login_email][user_activation]message .

However, after translating and setting the translation to completed, the emails are still sent in the original language.

One problem might be that the original language of the site is not english, it is hungarian. But WPML has identified the language as hungarian and is proposing the translations for english, which is exactly right, so I see no reason whatsoever why the emails are not getting translated.
I tried to use strings without special hungarian encoded characters, no difference either.

In the meantime I have tried to add english text for the custom emails and use WPML to translate to hungarian, but the result is the same, every time the english text from wp-options gets sent.

I have talked to the WPML support, they said they will also be in contact with you to sort this out. Thanks in advance.