The spec only requires a long-running conversation associated with a request that renders a JSF view to be automatically propagated to any faces request. The problem is if a conversation is begun using ajax calls. See also https://developer.jboss.org/people/mkouba/blog/2012/08/30/seam-vs-cdi-conversations--pay-attention-to-rerendering.

In theory, Weld could make use of FacesContext.getViewRoot().getViewMap() to store and load conversation id.