If you open wpGoogleMaps.php file at line #1135, you will see this code
function wpgmaps_admin_menu() {
add_menu_page('WPGoogle Maps', __('Maps','wp-google-maps'), 'manage_options', 'wp-google-maps-menu', 'wpgmaps_menu_layout', wpgmaps_get_plugin_url()."/images/map_app_small.png");
if (function_exists(wpgmza_pro_advanced_menu)) {
add_submenu_page('wp-google-maps-menu', 'WP Google Maps - Advanced Options', __('Advanced','wp-google-maps'), 'manage_options' , 'wp-google-maps-menu-advanced', 'wpgmaps_menu_advanced_layout');
}
add_submenu_page('wp-google-maps-menu', 'WP Google Maps - Settings', __('Settings','wp-google-maps'), 'manage_options' , 'wp-google-maps-menu-settings', 'wpgmaps_menu_settings_layout');
// add_options_page('WP Google Maps', 'WP Google Maps', 'manage_options', 'wp-google-maps-menu', 'wpgmaps_menu_layout');
}
Change ‘manage_options’ to capability you created with User Role Editor and included into ‘Author’ role and you will get it.