Would Luke have known about Stephen's death as a martyr by stoning, if it occurred? Luke was a traveling companion of Paul and closely associated with Paul. If a young Saul/Paul witnessed the death of Stephen, Luke would certainly have heard about it.
For evidence of Luke's association with Paul:
"Our dear friend Luke, the doctor, and Demas send greetings."
--Colossians 4:14 NIV
"Epaphras, my fellow prisoner in Christ Jesus, sends you greetings. And so do Mark, Aristarchus, Demas and Luke, my fellow workers."
--Philemon 24
2 Timothy 4:11 opens, "Only Luke is with me."
Second Timothy was written as Paul was a prisoner in Rome awaiting execution by beheading. It looks like Luke was in place to take Paul's final confession, if he needed one.
I don't see any doubt that Luke had access to the best information he could possibly have had, next to being an eyewitness. Luke had no need to make up any stories on this subject.
In addition, the stoning of Stephen was part of the persecution the early Christians in Jerusalem. This persecution caused many Christians to flee to other places, other Jewish communities, in the Roman world. This, in turn, helped to spread Christianity, and we know that this spreading of Christianity did happen.
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