Hi,
HikaShop has an API for developers here:
www.hikashop.com/support/documentation/6...r-documentation.html
By developing a plugin of the group "system" you could do what you want.
First, when someone adds something to the cart, you can implement the trigger onAfterCartSave(&$element) so that you can connect to the webhook, rest API or whatever filemaker has, to update the status of the products in $element->cart_products which contains the list of all the products in the cart and their new quantity (because the quantity can be changed, the product can be removed from the cart, etc).
Second, when someone places a order you can similarily implement the trigger onAfterOrderCreate or onAfterOrderUpdate to update the products stock of filemaker with $order->products
And finally, you can implement the trigger onAfterRoute() in your plugin and check the parameters given (so you can have filemaker pass a specific parameter so that the plugin can catch it and get the data of the stock being updated). Then, you can initialize the hikashop main helper and use such code to update the stock of the product:
include_once(rtrim(JPATH_ADMINISTRATOR,DIRECTORY_SEPARATOR).DIRECTORY_SEPARATOR.'components'.DIRECTORY_SEPARATOR.'com_hikashop'.DIRECTORY_SEPARATOR.'helpers'.DIRECTORY_SEPARATOR.'helper.php');
$product = new stdClass();
$product->product_id = $id_of_the_product;
$product->product_quantity = $new_stock_of_the_product;
$productClass = hikashop_get('class.product');
$productClass->save($product);
If the developer knows PHP, and has access to the filemaker integration documentation it shouldn't be a problem to develop such plugin.