$proxy = new SoapClient('http://magentohost/api/v2_soap/?wsdl');
$sessionID = $proxy->login('apiUser', 'apiKey');

$orderIncrementId = '100000016';

//Create invoice for order
$qty = array(
    array('order_item_id' => '15', 'qty' => '1')
);
$invoiceIncrementId = $proxy->salesOrderInvoiceCreate(
     $sessionID,
     $orderIncrementId,
     $qty);

//Capture invoice amount
$result = $proxy->salesOrderInvoiceCapture(
     $sessionID,
     $invoiceIncrementId
);