See the test shop at: www.dottedi.us/foxycart
I followed the instructions grabbing the example code from https://wiki.foxycart.com/v/2.0/api
and modifying customizing it to my test shop's parameters:
// $my_email and $my_password - these using a cookie to grab the email correctly
$foxy_domain = "dottedi.foxycart.com";
$foxyData = array();
$foxyData["api_token"] = "Rw8...RL2";
$foxyData["api_action"] = "customer_save";
// $foxyData["customer_id"] = "12345";
// OR use the email:
$foxyData["customer_email"] = "$my_email"; // this is good
$foxyData["customer_password"] = "$my_password"; // this is good
Leaving the rest of the default example intact the above works correctly if I click on "PROCEED TO CHECKOUT". It sends me to my sso.php page and creates the Foxycart user if the user doesn't exist. I verfied this by signing up for Order Desk Admin and signing in and viewing the customer list.
The document says that a success result is supposed to send the visitor back to the cart, to checkout with all customer data populated. How do you make this happen? Turning off the response messages does not help. Other than seeing success on my test site and seeing the customer is created, it doesn't go any further.