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Connect Bluetooth audio transmitter to Windows or Android to record

I have a Bluetooth audio transmitter/receiver (Ugreen CM403). In the transmitting mode, it converts analog input audio signal from a minijack (e.g. from a tape player) and sends it to my Bluetooth speaker. I want to record the audio received from the transmitter. To do that, I would like to connect the transmitter to my laptop (Windows 10 21H2) or my Android phone.

Neither the laptop nor my phone shows the transmitter in Bluetooth devices when I enable the pairing mode. When I use it with the speaker, both devices pair automatically once I enable pairing modes. I can’t find a way to do the same on Windows/Android. Is it possible? If not, is there some other way I can record the audio sent via Bluetooth?