Paul's goodbye speech to the elders of the Ephesian church at Miletus is recorded in Acts 20:18-35. It shows numerous indications of the accuracy of Luke's record, to the point that it seems likely that at least to some extent, in this case, Luke is recording Paul's exact words. It's striking how clearly we hear the authentic voice of Paul himself, recognizable from his letters. And yet there are also many reasons to think that Luke was not basing his history on the letters. (Among other things, the alleged contradictions that skeptics themselves bring up provide such reasons.)  

Here is Testify's video on some overlapping material:  https://www.youtube.com/watch?v=CkjdqvlLEZw&t=197s 

Here is my earlier discussion of the amazing undesigned coincidences connecting Acts 19-20 with I Corinthians, 2 Corinthians, and Romans.  https://www.youtube.com/watch?v=Xq7EDxPC3Fw