Thanks for the suggestions. Based on your replies, I changed the configuration to use SMTP - still using smtp.gmail.com.
I turned on email debugging. I can see that the "from" address that is sent to smtp.gmail.com is the survey administrator address (as expected), but when the invitation arrives in the recipient's inbox, the "from" address has been changed to the address of the authenticated user at smtp.gmail.com. (This seems reasonable - it prevents address spoofing.)
I did some exploring in the LS code. In file LimeMailer.php, I added a line of code after line 529 to include a reply-to header:
Code:
if (empty($updateDisable['from'])) {
$this->setFrom($event->get('from'));
// added code:
$this->addCustomHeader("Reply-To", $event->get('from'));
}
Adding the reply-to header here does what I need it to do. When the recipient clicks on the Reply button in email, the message is addressed to the survey administrator's email address instead of the account used to authenticate the smtp connection.
I will add it as a feature request if there isn't one already.