Problem: You want the language switcher in your WordPress site's menu to display the menu in English when a visitor is viewing the site in English, but currently, the menu does not change to English. Solution: We recommend translating your menu manually since it contains many custom links. You can find detailed instructions on how to do this by visiting the Translating Menus That Appear Different in Each Language section of our documentation. In your WordPress dashboard, go to Appearance > Menus, and click on the '+' sign next to your desired menu to add translations for each language.
If this solution does not resolve your issue or seems outdated, please check related known issues at https://wpml.org/known-issues/, verify the version of the permanent fix, and confirm that you have installed the latest versions of themes and plugins. If needed, do not hesitate to open a new support ticket for further assistance at WPML support forum.