Archive sent newsletters

You can do this using Rules. Views Send defines three events that you can use in Rules. Using the "After sending an individual email" event you can store everything about the message into a custom content type. Below is an example that just stores the title and body of the message as an article:

{ "rules_views_send_sent" : {
    "LABEL" : "Views Send Sent",
    "PLUGIN" : "reaction rule",
    "ACTIVE" : false,
    "REQUIRES" : [ "rules", "views_send" ],
    "ON" : [ "views_send_email_sent" ],
    "DO" : [
      { "entity_create" : {
          "USING" : {
            "type" : "node",
            "param_type" : "article",
            "param_title" : "E-mail sent [site:current-date] to [views-send-email-message:to_mail]: [views-send-email-message:subject]",
            "param_author" : "1"
          },
          "PROVIDE" : { "entity_created" : { "mail_log_entity" : "Mail log" } }
        }
      },
      { "data_set" : {
          "data" : [ "mail-log-entity:body:value" ],
          "value" : "[views-send-email-message:body]"
        }
      }
    ]
  }
}

Great that it worked for you.