Proxy a request using Guzzle, from A site to B site

Question

I'm trying to proxy a request from A site to B site, using guzzle.

-> send HTTP GET to A

...As data is coming from A...

-> send HTTP PUT to B Forward all content using streams.

How to do it? I tried this way, no data is sent to B:

$url_origin = '10.10.10.10/origin';

$url_dest = '20.20.20.20/dest';

$client_origin = new GuzzleClient();
$client_destination = new GuzzleClient();

$response_origin = $client_origin->request('GET', $url_origin, ['stream'=>true]);
$body_origin = $response_origin->getBody();

$dest_stream = Psr7\Utils::streamFor();

$response_dest = $client_destination->request('PUT', $url_dest, 
[
    'body' => $dest_stream,
    'stream'=>true,
    'read_timeout' => 10,
    'Content-Type' => 'application/octet-stream'
]);

while (!$body_origin->eof()) 
{
    $data = $body_origin->read(1024*1024);
    $dest_stream->write($data);
}

Then tried using only streams:

$url_origin = '10.10.10.10/origin';
$url_dest = '20.20.20.20/dest';

$client_origin = new GuzzleClient();
$client_destination = new GuzzleClient();

$stream = Psr7\Utils::streamFor();

$client_destination->request('PUT', $url_dest, 
[
    'body' => $stream, 
    'stream' => true, 
    'Content-Type' => 'application/octet-stream'
]);
$response_origin = $client_origin->request('GET', $url_origin, ['sink' => $stream]);

Same result... Any idea?