Add New screen of Admin Pages has a Permissions tab in the Advanced Options meta box.
Here you (admin) can check the roles that should have access to edit the admin page.
It is also possible to limit access by usernames. See this KB article.
You can log in using the user’s account that should not see “Admin Pages” menu in the WP admin, then pull down Screen Options from the top right and uncheck ‘Display the “Admin Pages” menu item?’.
One problem with this approach is that if your client is tech savvy enough or like the curious George, he/she may reverse this setting, then see the Admin Pages menu item and mess things up to their heart content.
The next method addresses this problem.
Adding the following using the Code Snippets plugin will ensure that the above Screen Options method does not function – meaning, only the admins will be able to access the Admin Pages admin menu.
add_filter( 'wu_apc_should_display_admin_menu', '__return_false' );
KB article regarding the last two methods is here.