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Not sure if I am understanding your problem but are you saying you can hear audio through the television or through your adaptor but not both at the same time.Most 3.5mm sockets are for headphones which often disconnects standard audio. If I am understanding your problem correctly then the easy answer may be to use a HDMI splitter which will send one hdmi signal to your extractor and a separate matching signal to your TV.However as mentioned above taking a digital audio from the HDMI cable and translating it to Bluetooth and then in your headset translating it back to sound again may delay the sound so the lipsync is off by a small amount.
Not sure if I am understanding your problem but are you saying you can hear audio through the television or through your adaptor but not both at the same time.
Most 3.5mm sockets are for headphones which often disconnects standard audio. If I am understanding your problem correctly then the easy answer may be to use a HDMI splitter which will send one hdmi signal to your extractor and a separate matching signal to your TV.
However as mentioned above taking a digital audio from the HDMI cable and translating it to Bluetooth and then in your headset translating it back to sound again may delay the sound so the lipsync is off by a small amount.
