Allow WordPress editor to access widgets

widgets.php

<?php

// Elevate caps since theme options are required to access widgets
$role = get_role('shop_manager'); 
$role->add_cap('edit_theme_options');

// Allow Editor widget access but remove themes, menu options and customizer.
function custom_admin_menu() {

    $user = new WP_User(get_current_user_id());     
    if (!empty( $user->roles) && is_array($user->roles)) {
        foreach ($user->roles as $role)
            $role = $role;
    }
		
    if($role == "editor") { 
       	global $submenu;
	 
	// Loop through to get the index of customizer. This makes sure its removed even if a plugin or something else changed it.
	if ( isset( $submenu[ 'themes.php' ] ) ) {
		foreach ( $submenu[ 'themes.php' ] as $index => $menu_item ) {
			if ( in_array( 'customize', $menu_item ) ) {
				unset( $submenu[ 'themes.php' ][ $index ] );
			}
		}
	}

	remove_submenu_page( 'themes.php', 'themes.php' );
	remove_submenu_page( 'themes.php', 'nav-menus.php' );
			
    } 
}
add_action('admin_menu', 'custom_admin_menu');

This works with WP 4.0+