Hi @tamar,
Thank you for letting me know. You are correct that it would be ideal for the inventory to sync to Facebook. In fact, we have that on the roadmap to include and hopefully that will soon be the case!
The good news here is that your site is where customers ultimately make their purchase. While it is possible for your product to show as being “in stock” on Facebook when it really isn’t, the customer would ultimately be directed to purchase on your WooCommerce store, where they would not be able to. In this way, it is not possible to sell a product that is truly out of stock, no matter what the status shows on Facebook.
Did you get a chance to update the stock levels on the Facebook side and see if your products are shown as “in stock”? Let me know!
Thanks,
Marcus