If the office is vacant, a non-cardinal may serve as Pro-tem Secretary of State, exercising the powers of the Secretary of State until a suitable replacement is found or the Pro-Secretary is made a cardinal in a subsequent consistory.
Pope Leo created him Cardinal Priest of Santi Marcellino e Pietro in the consistory of June 22, 1896, and he ceased to serve as Nuncio.
As of 2013, the most recent consistory for the creation of new cardinals took place on 24 November 2012 during which Pope Benedict XVI elevated 6 new cardinals - James Michael Harvey, Bechara Boutros al-Rahi, Baselios Cleemis, John Onaiyekan, Rubén Salazar Gómez and Luis Antonio Tagle.
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Griffin was created Cardinal-Priest of Ss. Andrea e Gregorio al Monte Celio by Pius XII in the consistory of 18 February 1946.
He was created Cardinal-Priest of Ss. Andrea e Gregorio al Monte Celio by John Paul II in the consistory of June 28, 1988.
Pope John Paul II created him Cardinal Deacon of San Teodoro in the consistory of June 30, 1979, whereupon he ceased to serve as Secretary of the Congregation for Bishops.
Pope Pius XI created him Cardinal-Priest of Santa Pudenziana in the consistory of 16 December 1935, and then Prefect of the Sacred Congregation of the Council on 22 July 1938.
Shortly afterwards, Pope Paul VI created him Cardinal-Deacon of SS. Nome di Maria al Foro Troiano in the consistory of 28 April 1969.