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The signal present on the wires that feed a speaker is alternating current -when there is audio presence- and not direct current as a led prefers to work with. Pushing the transmitter button alone does not produce audio at the receiver speaker wires.
The flash you see is from some inherent glitch.
If the two way radios are for voice communication, there is a remote chance you can succeed, by connecting -better two- counterparalleled leds instead of the speaker and set the volume full blast at receiver "B" while screaming your guts out at the microphone of transmitter "A". That may work only while screaming, not while pushing the transmit button.
Better use radiocontrol transmitter and receiver so the servo can move a contact to turn on the led.