joaquimP-2

Problem:
How to correctly convert my translation from using WP editor to ATE
Solution:
You would have to copy them one by one manually to insure a complete transition,

And keep in mind that you should never update/edit the translations using the page editor in second language, else, your translations will be lost.

Always use one method to translate and edit translations, in your case, I recommend sending the page for translation and edit it from ATE.
Relevant Documentation:
https://wpml.org/documentation/translating-your-contents/translation-editor-options/