You can always edit the PHP script that manages the email delivery and add headers to it. A sample form with the headers for your reference would be like the one below:
$to = 'firstname.lastname@example.org';
$subject = 'the subject';
$message = 'hello';
$headers = 'From: email@example.com' . "\r\n" .
'Reply-To: firstname.lastname@example.org' . "\r\n" .
'X-Mailer: PHP/' . phpversion();
mail($to, $subject, $message, $headers);
You basically need to define the "From:" field in order to have the email sent from the email address you wish to use.