I need to call a method annotated with @Asynchronous in EJB from a ConversationScoped bean. Inside this method I create instances of some classes using @Inject to inject ConversationScoped beans. Is it somehow possible to set the context of the asynchronous method to given Conversation?
I hope you can help me.
No, absolutely not. EJBs do per definition not run in web container, but in EJB container. In essence, having any web-related artifact/dependency (including javax.faces.* classes) inside an EJB class is a red alert. You're not supposed to inject/access any class from the client tier (the WAR) in the business tier (the EJB/EAR). Moreover, conversation scoped beans are tied to a HTTP request parameter and this information is nowhere available in an EJB container.
Whatever problem you're trying to solve and for which you incorrectly thought that this all would be the right solution, it has to be solved differently. As an educated guess, I think you just need to let the EJB fire a CDI event or take a callback argument.