Sharepoint - Copy attachments from list to another list

You can do it with following code:

foreach ($AttachName in $item.Attachments) 
{
    $spFile = $item.ParentList.ParentWeb.GetFile($item.Attachments.UrlPrefix + $AttachName);
    $newItem.Attachments.Add($AttachName, $spFile.OpenBinary());
}

Put that code after this line: $newItem["Initiator"] = $item["Initiator"] and it should be fine.