A quick php script that shows how to create a case and then a reply.

create_case_and_reply.php

<?php

function post($path, $json) {
  $ch = curl_init();
  
  curl_setopt($ch, CURLOPT_URL, "https://site.desk.com$path");
  curl_setopt($ch, CURLOPT_CUSTOMREQUEST, "POST");
  curl_setopt($ch, CURLOPT_USERPWD, "my-email:my-password");
  curl_setopt($ch, CURLOPT_POSTFIELDS, $json);
  curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
  curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, true);
  curl_setopt($ch, CURLOPT_HTTPHEADER, array(
    'Content-Type: application/json',
    'Content-Length: ' . strlen($json)) 
  );
  
  $result = curl_exec($ch);
  
  curl_close($ch);
  
  return $result;
}

// initial case
$json = json_encode(array(
  "subject" => "Test",
  "description" => "testing",
  "message" => array(
    "subject" => "Test",
    "body" => "Test",
    "direction" => "in",
    "to" => "[email protected]",
    "from" => "[email protected]",
    "status" => "received"
  ),
  "type" => "phone",
  "_links" => array(
    "customer" => array("href" => "/api/v2/customers/207020953")
  )
));

$case = json_decode(post('/api/v2/cases', $json));

// another reply
$json = json_encode(array(
  "subject" => "Re: Test",
  "body" => "Test",
  "direction" => "out",
  "to" => "[email protected]",
  "from" => "[email protected]",
  "status" => "sent"
));

$reply = post($case->_links->replies, $json);

echo $reply;