Best Audio Extractor + Bluetooth Transmitter Combo to get sound from Xbox Series S

Hello,

I have an Xbox Series S that I play using a computer monitor display.

My problem is that neither the Xbox S nor the monitor have internal speakers, so I need to find a way to connect my Xbox S to an external speaker. Specifically, I'd like to play my Xbox audio through a JBL Bluetooth Speaker that I already own.

To get over this problem, I bought the 4K Audio Extractor HDMI by OREI, because it allows me to connect a Bluetooth Transmitter to it, but the problem I have is that I'm still not getting any sound out of my JBL speakers after pairing it to the Bluetooth Transmitter.

Does anyone know if such a set-up can work? I've seen it work on Youtube when someone connected external speakers to the Audio Extractor using the Optical Output.

Does it make a difference whether the Bluetooth Transmitter connects to the Audio Extractor via the Aux (Analog) Output or Optical (Digital) Output for getting sound? The current Bluetooth Transmitter I'm using is called Cabletime BT Transmitter/Receiver, and I wonder if its a good or bad product. Reviews have been hard to find on it.

Any help or advice is much appreciated.

Thank you!

:)