Please try this code:-
$url = 'url_to_post';
$data = array("first_name" => "First name","last_name" => "last name","email"=>"[email protected]","addresses" => array ("address1" => "some address" ,"city" => "city","country" => "CA", "first_name" => "Mother","last_name" => "Lastnameson","phone" => "555-1212", "province" => "ON", "zip" => "123 ABC" ) );
$data_string = json_encode(array("customer" =>$data));
$ch = curl_init($url);
curl_setopt($ch, CURLOPT_POSTFIELDS, $data_string);
curl_setopt($ch, CURLOPT_HTTPHEADER, array('Content-Type:application/json'));
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$result = curl_exec($ch);
curl_close($ch);
echo "$result";