This thread is resolved. Here is a description of the problem and solution.
How to translate Advanced Custom Fields?
In order to translate Advanced CustoM Fields make sure to insall the plugins Translation Management and Advanced CustoM Fields Multilingual from your wpml.org account.
Then activate one of the WPML Translation Editors at WPML -> Settings -> How to translate posts and pages.
You will now be able to translate pages whihc include custom fields. It is not necessary to translate the custom fields groups, unless it is necessary to change the language for the custom field label on the backend accordingly.
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