Yes, Paul's acceptance by the apostles and early Christians was clear. Luke is generally accepted by scholars as the apostle who wrote down the
activities of the apostles
Here is one indication that Paul was clearly accepted as one of them:
"
22 Then tidings of these things came unto the ears of the church which was in Jerusalem: and they sent forth Barnabas, that he should go as far as Antioch.
23 Who, when he came, and had seen the grace of God, was glad, and exhorted them all, that with purpose of heart they would cleave unto the Lord.
24 For he was a good man, and full of the Holy Ghost and of faith: and much people was added unto the Lord.
25 Then departed Barnabas to Tarsus, for to seek Saul:
26 And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.
27 And in these days came prophets from Jerusalem unto Antioch.
28 And there stood up one of them named Agabus, and signified by the Spirit that there should be great dearth throughout all the world: which came to pass in the days of Claudius Caesar.
29 Then the disciples, every man according to his ability, determined to send relief unto the brethren which dwelt in Judaea:
30 Which also they did, and sent it to the elders by the hands of Barnabas and Saul. (Acts 11:22-30)
The old accuser likes to insert doubt, to the believer's detriment.. E.G. "Surely, you will not die"..