I have the following configuration:
As you can see, I have declared the annotation "@Local" on the service implementation without defining the local interface. Is it correct?
With EJB 3.1, the requirement for local interfaces was dropped. No need to write them unless you explicitly need them.
What is the best way to inject one EJB into another one?
Couple of things to write here:
With Java EE 6, Java Enterprise has changed. A new JSR defines a so-called managed bean (don't confuse with JSF managed beans) as a sort of minimum component that can still benefit from the container in terms of dependency injection and lifecycle management. This means: If you have a component and "just" want to use DI and let the container control its lifecycle, you do not need to use EJBs for it. You'll end up using EJBs if - and only if - you explicitly need EJB functionality like transaction handling, pooling, passivation and clustering.
This makes the answer to your question come in three parts: