How to use Spring Reactive WebSocket and transform it into the Flux stream?

There is some WebSocketClient example on Spring documentation:

WebSocketClient client = new ReactorNettyWebSocketClient();
client.execute("ws://localhost:8080/echo"), session -> {...}).blockMillis(5000);

Im not sure how to handle stream of incomming data? Inside that block {...}.

I mean: how can I filter incoming data and cast it into Flux?

Here is what I want to get.

@GetMapping("/stream", produces = MediaType.APPLICATION_STREAM_JSON_VALUE)
    public Flux<MyRecourse> getStreaming() {

    //  get some data from WebSocket (CoinCap service).
    //  Transform that data into MyRecourse object
    //  Return stream to a client 

}

Just take a look into that WebSocketSession param of the WebSocketHandler.handle() lambda:

/**
 * Get the flux of incoming messages.
 */
Flux<WebSocketMessage> receive();

See Spring WebFlux Workshop for more information.

UPDATE

Let's try this!

    Mono<Void> sessionMono =
            client.execute(new URI("ws://localhost:8080/echo"),
                    session ->
                            Mono.empty()
                                    .subscriberContext(Context.of(WebSocketSession.class, session))
                                    .then());

    return sessionMono
            .thenMany(
                    Mono.subscriberContext()
                            .flatMapMany(c -> c
                                    .get(WebSocketSession.class)
                                    .receive()))
            .map(WebSocketMessage::getPayloadAsText);

UPDATE 2

Or another option but with blocked subscription:

    EmitterProcessor<String> output = EmitterProcessor.create();

    client.execute(new URI("ws://localhost:8080/echo"),
            session ->
                    session.receive()
                            .map(WebSocketMessage::getPayloadAsText)
                            .subscribeWith(output)
                            .then())
            .block(Duration.ofMillis(5000));

    return output;

UPDATE 3

The working Spring Boot application on the matter: https://github.com/artembilan/sandbox/tree/master/websocket-over-webflux

The main code is like:

    EmitterProcessor<String> output = EmitterProcessor.create();

    Mono<Void> sessionMono =
            client.execute(new URI("ws://localhost:8080/echo"),
                    session -> session.receive()
                            .map(WebSocketMessage::getPayloadAsText)
                            .subscribeWith(output)
                            .then());

    return output.doOnSubscribe(s -> sessionMono.subscribe());