Wondering if the folder really is called Sent.
I used IMAP to list the folders and found that the folder is called INBOX.Sent.
I used the code below to list the folders:
$mailbox = "{".$mail->Host.":143/imap/novalidate-cert}";
$imapStream = imap_open($mailbox, $mail->Username, $mail->Password);
$mailboxes = imap_list($imapStream, $mailbox, '*');
echo "<pre>";
print_r($mailboxes);
And the code below to save a copy of the email in "Sent":
$mailbox = "{".$mail->Host.":143/imap/novalidate-cert}INBOX.Sent";
$imapStream = imap_open($mailbox, $mail->Username, $mail->Password);
imap_append($imapStream, $mailbox, $mail->getSentMIMEMessage(), "\\Seen");
imap_close($imapStream);
As in the function does not come the recipient made the following suitability:
$mailbox = "{".$mail->Host.":143/imap/novalidate-cert}INBOX.Sent";
$imapStream = imap_open($mailbox, $mail->Username, $mail->Password);
imap_append($imapStream, $mailbox, "To: ".$destinatario."\r\n".$mail->getSentMIMEMessage(), "\\Seen");
imap_close($imapStream);