Iniciar variável (Entity Manager) de um Managed Bean diretamenta pelo Faces-config.xml

public CadastroBean() {
		this.usuario = new Usuario();
		HttpServletRequest request = (HttpServletRequest) FacesContext.getCurrentInstance().getExternalContext().getRequest(); 
		this.manager = (EntityManager) request.getAttribute("entityManager");		
		dao = new UsuarioDAO(manager);		
	}

package control.filters;

import java.io.IOException;
import javax.persistence.EntityManager;
import javax.persistence.EntityManagerFactory;
import javax.persistence.Persistence;
import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.FilterConfig;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
/** 
 * @author Hromenique Cezniowscki Leite Batista</br></br>
 * Filtro que comanda o ciclo de vida de um EntityManager que é passado para as classes de négocios
 *
 */
public class EntityManagerFilter implements Filter {
	
	private EntityManagerFactory factory; 
	
	public void doFilter(ServletRequest request, ServletResponse response, FilterChain chain) throws IOException, ServletException {
		EntityManager manager = this.factory.createEntityManager();
		//atributo a ser passado junto com o request
		request.setAttribute("entityManager", manager);
		manager.getTransaction().begin();
		
		chain.doFilter(request, response);
		
		try{
			manager.getTransaction().commit();
		}
		catch (Exception e) {
			manager.getTransaction().rollback();
		}
		finally{
			manager.close();
		}		
	}
	
	public void init(FilterConfig arg0) throws ServletException {
		this.factory = Persistence.createEntityManagerFactory("trab_solucoes_web");
		
	}
	
	public void destroy() {
		this.factory.close();
		
	}
}

import javax.faces.context.FacesContext;
import javax.faces.event.ActionEvent;
import javax.persistence.EntityManager;
import javax.servlet.http.HttpServletRequest;

import model.dao.classes.UsuarioDAO;
import model.entities.Usuario;

/**
 * @author Hromenique Cezniowscki Leite Batista</br> </br>
 * Classe que desempenha o papel de Managed Bean da página cadastro.xhtml. Responsável pela regras de négocios para cadastro de novos usuários.
 *
 */
public class CadastroBean {

	/*VARIÁVEIS*/
	private EntityManager manager;
	private Usuario usuario;
	private String confirmacaoEmail;
	private String confirmacaoSenha;	
	private UsuarioDAO dao;

	
	/*CONSTRUTORES*/
	public CadastroBean() {
		this.usuario = new Usuario();
		//HttpServletRequest request = (HttpServletRequest) FacesContext.getCurrentInstance().getExternalContext().getRequest(); 
		//this.manager = (EntityManager) request.getAttribute(&quot;entityManager&quot;);		
		dao = new UsuarioDAO(manager);		
	}
	
	/*MÉTODOS*/
	public void salvar(ActionEvent event){
		//No ínicio o login é igual ao email.
		this.usuario.setLogin(this.usuario.getEmail());
		dao.salvar(this.usuario);
		//return &quot;sucesso&quot;;
	}

	public Usuario getUsuario() {
		return usuario;
	}

	public void setUsuario(Usuario usuario) {
		this.usuario = usuario;
	}

	public String getConfirmacaoEmail() {
		return confirmacaoEmail;
	}

	public void setConfirmacaoEmail(String confirmacaoEmail) {
		this.confirmacaoEmail = confirmacaoEmail;
	}

	public String getConfirmacaoSenha() {
		return confirmacaoSenha;
	}

	public void setConfirmacaoSenha(String confirmacaoSenha) {
		this.confirmacaoSenha = confirmacaoSenha;
	}

	public UsuarioDAO getDao() {
		return dao;
	}

	public void setDao(UsuarioDAO dao) {
		this.dao = dao;
	}

	public EntityManager getManager() {
		return manager;
	}

	public void setManager(EntityManager manager) {
		this.manager = manager;
	}
}

<?xml version="1.0" encoding="UTF-8"?>
<faces-config version="1.2" xmlns="http://java.sun.com/xml/ns/javaee"
 xmlns:xi="http://www.w3.org/2001/XInclude"
 xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-facesconfig_1_2.xsd">
 
 <application>
  <view-handler>com.sun.facelets.FaceletViewHandler</view-handler>
 </application>

 <!-- ####################### BEANS ###################################################################################################### -->
 <managed-bean>
  <managed-bean-name>cadastroBean</managed-bean-name>
  <managed-bean-class>control.beans.CadastroBean</managed-bean-class>
  <managed-bean-scope>request</managed-bean-scope> 
  
  <managed-property>
  <property-name>manager</property-name>
  <value>#{requestScope.entityManager}</value> <!-- AQUI É ONDE EU QUERO INICIAR O BEAN COM OBJETO PASSADO VIA FILTRO, UTILIZANDO INJEÇÃO DE DEPENDÊNCIA -->
  </managed-property>
 </managed-bean> 
 </faces-config>