JSF managed-bean EJB injection

You are mixing the responsibilities of EJBs and JSF managed beans. The faces-config.xml registers only JSF artifacts, such as managed beans and not EJBs. Your registration in faces-config.xml

<managed-bean>
    <managed-bean-name>personManager</managed-bean-name>
    <managed-bean-class>ejb.PersonManager</managed-bean-class>
    <managed-bean-scope>session</managed-bean-scope>
</managed-bean>

does basically exactly the same as

@ManagedBean
@SessionScoped
public class PersonManager {
    // ...
}

In other words, you’re registering the class as a JSF managed bean which is available in views by #{personManager}. This does not represent the same instance as is managed by the EJB container. You can and should not use faces-config.xml to register EJBs. There you use the annotations from the javax.ejb package for, such as @Stateless and @Stateful. That’s all you need to register an EJB.

Actually, registering JSF managed beans in faces-config.xml is an old JSF 1.x way which has in JSF 2.x been replaced by the new @ManagedBean annotation.

---

Update the proper approach would be:

View (the Facelets file):

<h:form>
    <h:inputText value="#{personManager.person.name}" />
    ...
    <h:commandButton value="Save" action="#{personManager.save}" />
    <h:messages />
</h:form>

Controller (the JSF managed bean):

@ManagedBean
@ViewScoped
public class PersonManager implements Serializable {

    private Person person;

    @EJB
    private PersonService personService;

    @PostConstruct
    public void init() {
        person = new Person();
    }

    public void save() {
        personService.create(person);
        FacesContext.getCurrentInstance().addMessage(null,
            new FacesMessage("Person successfully created, new ID is " + person.getId()));
    }

    // ...
}

Model (the JPA entity):

@Entity
public class Person implements Serializable {

    @Id
    private Long id;

    private String name;

    // ...
}

Service (the stateless EJB):

@Stateless
public class PersonService {

    @PersistenceContext
    private EntityManager em;

    public void create(Person person) {
        em.persist(person);
    }

    // ...
}