This thread is resolved. Here is a description of the problem and solution.
Problem: I can't send strings from WPML > String Translation > Translate texts in admin screens to WPML > String Translation.
Solution: Most of the time, the main issue is that the max input vars value needs to be increased which is step 3 in the list here: https://wpml.org/forums/topic/not-able-to-send-admin-text-to-string-translator/#post-4349651
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