Then Paul was a liar:
Am I not an apostle? am I not free? have I not seen Jesus Christ our Lord? are not ye my work in the Lord? If I be not an apostle unto others, yet doubtless I am to you: for the seal of mine apostleship are ye in the Lord. (1 Corinthians 9:1-2 KJV)
Apostles were witness to the resurrected Lord. When the witnesses died, so did the office. There was nothing to pass down since the eye witness was personal and only given to those chosen by God. You had to be there.
Acts 10:39-42, “And we are witnesses of all things which he did both in the land of the Jews, and in Jerusalem; whom they slew and hanged on a tree: Him God raised up the third day, and shewed him openly; Not to all the people, but unto witnesses chosen before of God, even to us, who did eat and drink with him after he rose from the dead. And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead.”
1 Cor. 15:4-8, “And that he was buried, and that he rose again the third day according to the scriptures: And that he was seen of Cephas, then of the twelve: After that, he was seen of above five hundred brethren at once; of whom the greater part remain unto this present, but some are fallen asleep. After that, he was seen of James; then of all the apostles. And last of all he was seen of me also, as of one born out of due time.”