As plugin shows only one menu item, I think that creating new submenu to it is too much. Let's move 'Horizontal Scrolling' menu item from the 'Settings' menu to the 'Tools' menu. As 'Tools' menu is available for all users you can limit access to the 'HS' menu item easy. What you should do?
change lines above to
add_management_page('Horizontal scrolling announcement', 'Horizontal Scrolling', 'manage_announcements', __FILE__, 'HSA_admin_options' );
add_management_page('Horizontal scrolling announcement', '', 'manage_announcements', "horizontal-scrolling-announcement/horizontal-scrolling-setting.php",'' );
Also you need to replace all occurrences of 'options-general.php' to the 'tools.php':
line #156 should become:
$mainurl = get_option('siteurl')."/wp-admin/tools.php?page=horizontal-scrolling-announcement/horizontal-scrolling-announcement.php";
line #285:
<td align="left" valign="middle"><a href="tools.php?page=horizontal-scrolling-announcement/horizontal-scrolling-announcement.php&DID=<?php echo($data->hsa_id); ?>">Edit</a> <a onClick="javascript:_hsadelete('<?php echo($data->hsa_id); ?>')" href="javascript:void(0);">Delete</a> </td>
Lines 2,3 at button.php waits for your intervention with the same replace of 'options-general.php' with 'tools.php' too.