Advanced Notifications for WooCommerce extension for WooCommerce lets you set up order and stock notifications for users other than the admin.

WooCommerce Advanced Notifications Features

• Purchases – Sent when an order has been purchased, not when the original order is created. These notifications contain order and customer details.
• Low stock – Sent when an item is getting low is stock
• Out of stock – Sent when an item is out of stock.
• Backorders – Sent when an item is backordered (stock < 0 ).
• Refunds – Sent when a refund is issued.