Set a variable to using in redirected page

by

I think wp_login is executing before functions.php is actually opened, thus not setting the global variable. One possible solution to this is instead append to the URL:

function open_menu($user_login) {
    wp_redirect(home_url().'?menu_open=true');
    exit;
}
add_action('wp_login', 'open_menu');

Then you could get that value via 

if(isset($_GET['menu_open']) && $_GET['menu_open'])