There is a noteworthy scholarly position that Matthew was the first Gospel writtenthe first Gospel written. As such, it may have even been the first New Testament book written. If this is correct, it is likely that Matthew was of unparallelled importance in the early church, and that it would have been a major source of information about Jesus for most (if not all) of the remainder of the books in the New Testament.1
I read a JETS article a while back which argued via literary connections that Matthew was almost certainly the source of Paul's teachings on eschatology in 1 and 2 Thessalonians.2 I occasionally come across other evidence that Paul used Matthew as his primary source on Jesus' teachings.3 More recently, one of my professors commented that he is becoming increasingly "struck by" the literary connections between Paul's writings and Matthew.
My question here is: What is the primary evidence in support of this theory, that Paul relied heavily on Matthew for his understanding of Jesus' teachings? I have the data point from 1 & 2 Thessalonians, and the generic argument that Matthew was early and important, but beyond that all I have are vague impressions and general comments from others.
1) Of course, this is not the only scholarly position, but it is the one I am interested in for this question.
2) As most hermeneutics books will point out, recognizing intertextuality is an important step in the interpretive process -- whether explicit ("as it is written") or implicit (such as allusions, echoes, etc.) There are different approaches to identifying the latter, but in general it is agreed that if two passages share a large number of identical (or very similar) words, and context permits, it is likely that a reference was intended by the author.
3) For example, the way Matthew crafts his Gospel is very unique, and some of his major themes also have a unique prominence in Paul's writings. In other places (if memory serves), Paul's citations of what Jesus said and did while on earth are only found in Matthew.
NOTE: For this question, please assume that all 13 canonical Pauline letters were authored by Paul, and that Paul was a Christian (i.e. not at odds with Jesus and His teachings.)
NOTE: Please don't take me down the rabbit trail of why Mark is earlier than Matthew, or why Paul's eschatology is different than Jesus', or why Scripture is supernatural and the normal conventions of human language do not apply. I'm looking for the arguments in favor of a particular perspective.