PHPMailer with locaweb - You are not saving the emails sent to my LocaWeb account

There is no way to be saved, as is the role of the email manager you are using.

With PHPMailer , you are not using any, just authenticating to send the email, so there is no copy left.

Some options:

• Send a copy to you , and make a filter on your manager, which identifies that the email was sent by you, and then save it to the Sent folder.
• Use IMAP

Example of sending copies

Sending as a copy:

$mail->addCC('[email protected]');

Sending as a hidden copy:

$mail->addBCC('[email protected]');

IMAP (example with GMAIL)

# verificação se o e-mail foi enviado ou teve erros
if (!$mail->send()) {
    echo "Mailer Error: " . $mail->ErrorInfo;
} else {
    echo "Message sent!";
    $save_result = save_mail($mail); # chama a função para envio da cópia via IMAP
    if ($save_result) {
        echo "Message saved!";
    }
}
 # função para chamar IMAP: https://php.net/manual/en/book.imap.php
function save_mail($mail) {
    # Você pode enviar para a pasta de enviados ou alguma tag
    $path = "{imap.gmail.com:993/imap/ssl}[Gmail]/Sent Mail";
    # autenticando
    $imapStream = imap_open($path, $mail->Username, $mail->Password);
    # você pode usar imap_getmailboxes($imapStream, '/imap/ssl') para obter a lista de pastas e tags

    //Can be useful if you are trying to get this working on a non-Gmail IMAP server.
    $result = imap_append($imapStream, $path, $mail->getSentMIMEMessage());
    imap_close($imapStream);
    # retorna o resultado
    return $result;
}

Example via IMAP

More

Some links about PHPMailer:

PHPMailer

Shipping mail with multiple senders and recipients

HTML email image in PHPMailer

Differences in PHPMailer functions