No Other Name Under Heaven has been Given to Men, Whereby We Must be Saved

No faith in God can for long survive pure and unalloyed without the support of faith in Christ. "No one knoweth who the Son is, but the Father: and who the Father is, but the Son and to whom the Son will reveal Him" (Luke x. 22). "Now this is eternal life: That they may know thee, the only true God, and Jesus Christ whom thou has sent" (John xvii. 3). Nobody, therefore, can say: "I believe in God, and that is enough religion for me," for the Savior's words brook no evasion: "Whosoever denieth the Son, the same hath not the Father. He that confesseth the Son hath the Father also" (1 John ii. 23).
In Jesus Christ, Son of God made Man, there shone the plentitude of divine revelation. "God, who at sundry times and in divers manners, spoke in times past to the fathers by the prophets last of all, in these days hath spoken to us by His Son" (Heb. i. 1). The sacred books of the Old Testament are exclusively the word of God, and constitute a substantial part of his revelation; they are penetrated by a subdued light, harmonizing with the slow development of revelation, the dawn of the bright day of the redemption. As should be expected in historical and didactic books, they reflect in many particulars the imperfection, the weakness and sinfulness of man. But side by side with innumerable touches of greatness and nobleness, they also record the story of the chosen people, bearers of the Revelation and the Promise, repeatedly straying from God and turning to the world. Eyes not blinded by prejudice or passion will see in this prevarication, as reported by the Biblical history, the luminous splendor of the divine light revealing the saving plan which finally triumphs over every fault and sin. It is precisely in the twilight of this background that one perceives the striking perspective of the divine tutorship of salvation, as it warms, admonishes, strikes, raises and beautifies its elect. Nothing but ignorance and pride could blind one to the treasures hoarded in the Old Testament.
Whoever wishes to see banished from church and school the Biblical history and the wise doctrines of the Old Testament, blasphemes the name of God, blasphemes the Almighty's plan of salvation, and makes limited and narrow human thought the judge of God's designs over the history of the world: he denies his faith in the true Christ, such as He appeared in the flesh, the Christ who took His human nature from a people that was to crucify Him; and he understands nothing of that universal tragedy of the Son of God who to His torturer's sacrilege opposed the divine and priestly sacrifice of His redeeming death, and made the new alliance the goal of the old alliance, its realization and its crown.
The peak of the revelation as reached in the Gospel of Christ is final and permanent. It knows no retouches by human hand; it admits no substitutes or arbitrary alternatives such as certain leaders pretend to draw from the so-called myth of race and blood. Since Christ, the Lord's Anointed, finished the task of Redemption, and by breaking up the reign of sin deserved for us the grace of being the children God, since that day no other name under heaven has been given to men, whereby we must be saved (Acts iv. 12). No man, were every science, power and worldly strength incarnated in him, can lay any other foundation but that which is laid: which is Christ Jesus (1 Cor. iii 11). Should any man dare, in sacrilegious disregard of the essential differences between God and His creature, between the God-man and the children of man, to place a mortal, were he the greatest of all times, by the side of, or over, or against, Christ, he would deserve to be called prophet of nothingness, to whom the terrifying words of Scripture would be applicable: "He that dwelleth in heaven shall laugh at them" (Psalms ii. 3).

From: Encyclical of Pope Pius XI. on the Church and the German Reich, "Mit brennender Sorge", Passion Sunday, March 14, 1937

See also: There is no salvation through anyone else than Jesus Christ

Conclusion:
Muhammad is a prophet of nothingness and does not have eternal life, for he dares, as a mortal, to place himself sacrilegiously over and against Christ the God-man. He denies the Son and therefore does not have nor know the Father, the ONE GODHEAD.