The Source of the Apostles' Teaching
Their teachings were also from God, given them through the Holy Spirit.
John 14:26; 16:13 - Jesus promised the apostles that the Holy Spirit would come and teach them all things, guide them into all truth, and remind them of Jesus' teachings.
Matthew 10:19,20 - When they taught, they were not teaching from themselves, but the Spirit of the Father spoke through them.
[2 Timothy 3:16,17; Acts 1:5,8; 2:1-4,33; Matthew 28:18-20; 2 Peter 3:2; Revelation 1:1]
So the apostles' teachings came from the same source as did Jesus' teaching. All of them spoke the will of God as revealed to them by the Holy Spirit. The apostles' teaching was as accurate and as authoritative as was Jesus' teaching. All spoke with the infallible authority of God.
If this is not so, then in fact we do not even really know what Jesus Himself taught, since He never wrote any of the Bible. All we have are records which apostles and prophets wrote of what He said and did. If we accept what they record of Jesus' teachings, why not accept the other teaching that the Spirit guided them to write?