This has no sense at all, sending an e-mail is easy and squirrel mail is only a mail client.
It is like you would say that sending an e-mail to outlook would not be possible...
I'm using this PHP code to send mails and it works perfectly for me:
$mime_boundary=md5(time());
$headers = "Date: ".date("l j F Y, G:i")."\n";
$headers .= "MIME-Version: 1.0\n";
$headers .= "From: your_company_name <aaa@bbb.com>\n";
$headers .= "MIME-Version: 1.0\n";
$MailContent = "asdasdasdasdasda";
$sentOK = mail("aaa@bbb.com","Subject",$MailContent,$headers);
Look for samples in the Internet (use google) to get more examples on how to send mails using PHP and see if the mail address used with the squirrel mail client has not been blocked in your mail server.
Good luck!