Nor did Xavier have the chance to read the reference in footnote  to LG (Cfr. Epist. S.S.C.S. Officii ad Archiep. Boston.: Denz. 3 86972), the **LETTER OF THE SACRED CONGREGATION OF THE HOLY OFFICE ** which teaches: In His infinite mercy God has willed that the effects, necessary for one to be saved, of those helps to salvation which are directed toward man’s final end, not by intrinsic necessity, but only by divine institution, can also be obtained in certain circumstances when those helps are used only in desire and longing. This we see clearly stated in the Sacred Council of Trent, both in reference to the sacrament of regeneration and in reference to the sacrament of penance .
The same in its own degree must be asserted of the Church, in as far as she is the general help to salvation. Therefore, that one may obtain eternal salvation, it is not always required that he be incorporated into the Church actually as a member, but it is necessary that at least he be united to her by desire and longing.
However, this desire need not always be explicit, as it is in catechumens; but when a person is involved in invincible ignorance God accepts also an implicit desire, so called because it is included in that good disposition of soul whereby a person wishes his will to be conformed to the will of God.
These things are clearly taught in that dogmatic letter which was issued by the Sovereign Pontiff, Pope Pius XII, on June 29, 1943, On the Mystical Body of Jesus Christ . For in this letter the Sovereign Pontiff clearly distinguishes between those who are actually incorporated into the Church as members, and those who are united to the Church only by desire.
Discussing the members of which the Mystical Body is composed here on earth, the same august Pontiff says: "Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed."
Toward the end of this same encyclical letter, when most affectionately inviting to unity those who do not belong to the body of the Catholic Church, he mentions those who “are related to the Mystical Body of the Redeemer by a certain unconscious yearning and desire,” and these he by no means excludes from eternal salvation, but on the other hand states that they are in a condition “in which they cannot be sure of their salvation” since “they still remain deprived of those many heavenly gifts and helps which can only be enjoyed in the Catholic Church” . With these wise words he reproves both those who exclude from eternal salvation all united to the Church only by implicit desire, and those who falsely assert that men can be saved equally well in every religion ; also Pope Pius IX in the encyclical letter, Quanto conficiamur moerore .
But it must not be thought that any kind of desire of entering the Church suffices that one may be saved. It is necessary that the desire by which one is related to the Church be animated by perfect charity. Nor can an implicit desire produce its effect, unless a person has supernatural faith: “For he who comes to God must believe that God exists and is a rewarder of those who seek Him” (Heb. 11:6). The Council of Trent declares : “Faith is the beginning of man’s salvation, the foundation and root of all justification, without which it is impossible to please God and attain to the fellowship of His children” .
 Denzinger, nn. 797, 807.
 AAS, Vol. 35, an. 1943, p. 193 ff.
 AAS, 1. c., p. 243
 cf. Pope Pius IX, Allocution, Singulari quadam, in Denzinger, n. 1641 ff.
 Denzinger, n. 1677
 Council of Trent, Session VI, chap. 8
 (Denzinger, n. 801I believe that if Francis Xavier had known these teachings of the Magisterium, he would have accepted to these teachings with joy.