The documentation of the camel-ahc component states:
... All headers from the IN message will be copied to the OUT message, so headers are preserved during routing. Additionally Camel will add the HTTP response headers as well to the OUT message headers.
However this is not true. Camel headers are not copied from the in to the out message.
I have looked up other components doing http requests (http4 and cxf) and these components do copy the headers from the in to the out message.