This thread is resolved. Here is a description of the problem and solution.
Problem: The language switcher short code is on page 1. We need to pass the selected language_code in the url along with the parameters (key1, key2, key3, key4) being passed to page 2. Screen shot #2 Page 2 illustrates the problem we are having. The language_code is passed, but the parameters are not.
Solution: I understand that you need to pass the parameters (key1, key2, key3, key4) in the URL to the other language. If this is correct, then you can do this by following this steps: https://wpml.org/documentation/getting-started-guide/language-setup/language-switcher-options/#preserving-url-parameters
This is the technical support forum for WPML - the multilingual WordPress plugin.
This topic is split from https://wpml.org/forums/topic/drop-down-menu-wont-drop-down/