As I understand your question, it deals with the identification of the medium of divine Revelation. I will divide my answer in two parts, providing some broader context in the first.
Stages and structure of the medium of divine Revelation
In the case of "sealed" views of divine Revelation, such as those held by Jews, Christians and Muslims, i.e. of a divine Revelation that has been fully completed in the past, the medium of Revelation which must be identified includes two stages:
the original medium through which God has revealed in the past, and
the proximate medium that currently holds the "deposit" of what God has revealed through the original medium and, in some views, provides authoritative identification and interpretation of that Revelation.
Regarding the original medium, and focusing on the "ultimate" such medium, Jews, Christians and Muslims identify it with Moses, Jesus Christ and his Apostles, and Mohammed respectively.
Regarding the proximate medium, there are two main views on its structure:
A. It is a book plus a tradition, both interpreted by a divinely assisted and authoritative magisterium, which is the belief held by Rabbinic Jews and Roman Catholics/Eastern Orthodox.
B. It is just a book, which is the belief held by Karaite Jews, Christian Protestants and Quranist Muslims.
The views of the main denominations of Islam, i.e. Sunni and Twelver Shia, seem to be intermediate between these two, as they recognize the Quran and also the oral traditions about Mohammed (hadith), which were eventually written down in collections of books, different for each denomination.
In the Catholic Church, the doctrine of the proximate medium of Revelation was stated magisterially first by the Ecumenical Council of Trent and then by the Ecumenical Council Vatican I, in its Dogmatic Constitution "Dei Filius", which quotes Trent:
"Furthermore, this supernatural revelation, according to the faith of
the universal Church, declared by the holy Synod of Trent, is
contained "in the written books and the unwritten traditions which,
received by the Apostles from the mouth of Christ himself, or from the
Apostles themselves by the dictation of the Holy Spirit, have come
down to us, transmitted as it were from hand to hand" [Council of
Trent]." (ch. 2 "On Revelation")
"For the doctrine of faith, which God has revealed, has not been
proposed as a philosophical invention to be perfected by human
ingenuity, but has been delivered as a divine deposit to the Spouse of
Christ, to be faithfully guarded and infallibly declared (fideliter
custodienda et infallibiliter declaranda)." (ch. 4 "On faith and
Identification of the medium of divine Revelation
Clearly the "strict" definition of faith, e.g. by the Ecumenical Council Vatican I in its Dogmatic Constitution "Dei Filius", ch. 3 "On faith":
"The Catholic Church professes that this faith, which is the beginning
of human salvation, is a supernatural virtue, by means of which, with
the inspiration and assistance of the grace of God, we believe that
the things revealed by Him are true, not because the intrinsic truth
of the things has been perceived by the natural light of reason, but
because of the authority of God Himself who reveals them, who can
neither deceive nor be deceived."
cannot apply to the identification of the medium of divine Revelation, lest the epistemic situation be circular, as a person should have to identify M as the medium through which God reveals by an assent to the truth that "God reveals through M" based on the authority of God who revealed (through M) said truth (i.e. that He reveals through M)! Thus, the medium of divine Revelation must be rationally identified, based on its motives of credibility.
"Dei Filius", in line with its quoted teaching on the proximate medium of divine Revelation, states clearly that only the Catholic Church exhibits real motives of credibility of being such a medium:
"And, that we may be able to satisfy the obligation of embracing the
true faith and of constantly persevering in it, God, through his
only-begotten Son, has instituted the Church, and has bestowed on it
manifest notes of that institution, so that it may be recognized by
all as the guardian and teacher (custos et magistra) of the revealed
word. For to the Catholic Church alone belong all those things, so
many and so marvelous, which have been divinely established for the
evident credibility of the Christian faith. Moreover, the Church by
itself, because of its marvelous propagation, its exceptional
holiness, and its inexhaustible fruitfulness in all that is good,
because of its Catholic unity and invincible stability, is a great and
perpetual motive of credibility and an irrefutable evidence
(testimonium) of its own divine mission." (ch. 3 "On faith")
Addendum: A podcast of a lecture on the motives of credibility mentioned in the last quote from Constitution Dei Filius by Dr. Lawrence Feingold, Associate Professor of Philosophy & Theology at Kenrick-Glennon Seminary in Saint Louis, Missouri, is available here:
The handout provided at the lecture is available as a pdf file here: