This thread is resolved. Here is a description of the problem and solution.
Problem: I cannot display the translations completed in the Advanced Translation Editor although in the settings I have selected "Use WPML's Advanced Translation Editor" and I have synchronized the content. The translations are visible in the ATE but are not displayed on the website.
Solution: Make a small change to the original page, update the translation, and check again the translated page.
This is the technical support forum for WPML - the multilingual WordPress plugin.