Sorry, but with the free version you can't make menu permissions less restrictive; you can only restrict access further. This is because each menu typically has at least two capability checks - one in the admin menu itself (Admin Menu Editor can change this) and one in the plugin/theme/WP code that created the menu. Usually, the second check can't be changed or overridden without editing the source code.
Instead of changing this permission in AME, try adding the required capability to the Editor role. You can do that with a role management plugin like User Role Editor.
(The Pro version of Admin Menu Editor gets around this problem by automatically giving the required capability to each enabled role.)