This thread is resolved. Here is a description of the problem and solution.
Problem:
The client wants to retrieve the translated string from WPML >> String Translation page using the wpml_translate_single_string hook but it was returning the default language string instead of the translation.
Solution:
First, registering the string using the wpml_register_single_string hook solved the issue.
Relevant Documentation:
https://wpml.org/wpml-hook/wpml_register_single_string/
https://wpml.org/wpml-hook/wpml_translate_single_string/
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