In order to make the listing in shop B go out-of-stock automatically, you need to set the following items:

1. Set up stock level for your SKU

Go to Product>Product Master>Product Maintenance

You can set stock levels in system, or you can export SKUs to excel, modify the stock levels and upload back to system.

2.  Set up "auto deduct stock" and "auto out-of-stock" for both A, B shop

Go to Channels>Sales Channel, click the gear button on your shop.
1) Enable "Central Stock level Auto-deduction when Order (Paid only) is created" under "Central Stock Level Settings"

2) Turn on "Out of Stock Setting", then set "Auto stock-level trigger OS/Release function (Auto OS)" and "Change the out-of-stock GTC listing to OS status" to "yes"

Let's say both listings in shop A and B has a quantity equal to 1, and SKU stock level is also 1.

When listing in shop A sells, the system will deduct stock level for the SKU, when the stock level reaches 0, auto OS is triggered for shop B, so listing in shop B will also go 0.

Please note that if SKU stock level hasn't reached 0, auto OS for shop B will not be triggered.