Does the Book of Mormon Plagiarise the KJV New Testament?

A few days ago, I was stopped on the street of Cork city by a member of Ballincollig Baptist Church, a fundamentalist, KJV only group which is headed by Craig Ledbetter, an individual who is grossly ignorant of both biblical exegesis and engages in a campaign of deception against The Church of Jesus Christ of Latter-day Saints. In the course of this conversation, he claimed that the Book of Mormon plagiarised the New Testament of the King James, although he could not give any examples. I gave him my email address, asking him to substantiate his claim. To see his examples of plagiarism (which is nothing short of “parallelomania”), see here.