How to reference JSF @ManagedBean inside Spring MVC @Controller

From a Spring MVC @Controller, I need to be able to call a JSF @ManagedBean.

The problem seems to be that the @ManagedBean is not visible in the Spring ApplicationContext. Is there any way to do make the following accessible:

Code:

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@ManagedBean(name = "jsfService")
@ViewScoped
public class JsfServiceImpl implements JsfService {

    @ManagedProperty(value = "#{jsfDao}")
    private JsfDao jsfDao;

    ...

    private Long selectedId;

    public void setSelectedId(Long selectedId) {
        this.selectedId = selectedId;
    }

    ...

    public String doStuff() {
        FacesContext context = FacesContext.getCurrentInstance();
        Flash flash = context.getExternalContext().getFlash();
        flash.put("stuffContext", String.valueOf(this.selectedId));
        flash.put("backView", context.getViewRoot().getViewId());
        return "/do/stuff";
    }

}

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... so it could be accessed in a @Controller like so:

Code:

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@Controller
public class JsfRedirectController implements ApplicationContextAware {

    private ApplicationContext applicationContext;
   
    @RequestMapping("/do-jsf-stuff/{id}")
    public void doJsfStuffById(@PathVariable("id") long id) {
        JsfServiceImpl jsfService = applicationContext.getBean(JsfServiceImpl.class);
        jsfService.setSelectedId(id);
        jsfService.doStuff();
    }

    public void setApplicationContext(ApplicationContext applicationContext) throws BeansException {
        this.applicationContext = applicationContext;
    }
   
}

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I have set the following in faces-config.xml, but that seems only to make Spring beans available to JSF and not the other way around:

HTML Code:

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 <application>
  <el-resolver>org.springframework.web.jsf.el.SpringBeanFacesELResolver</el-resolver>
 </application>

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