There is no acvtual proof that all the writing attributed to Saul were written by the same person.
Often times, in the Bible one figure is in fact a recollection of several people. And Sometimes, One person is showed as several figures with different.
One telling example of that is the figure of Mary Magdalene whose sometimes refered to as Mary of Magdala or The Magdalene. Several names, one person. In 591 A.C. Pope Gregory I assimilated her to the unnamed sinner who annoited Jesus' feets (Luke 7 ; 37-40) and even Mary of Bethany, sister of Lazarus and Martha, who also annoits Jesus' feets in John 11 ; 1-2. In 1969, Pope Paul VI officialy stated that these 3 persons were different and that Mary Magdalene shouldn't be refered to as a repented sinner. Mopst biblical scholars agree with him.
The Bible is not like other books, it changes over time. The biblical canon was fixed in the late XVIth Century, before that, some writing that are in your bible weren't in the Bible and some that aren't in your bible were in the Bible. And, I'm not an expert in that area and I don't know if your an evangelist, a baptist, an pentecotist, or whatever but I'm pretty sure that my catholic Bible (yes I do posses a Bible, even if I'm an atheist) is different from your Bible.
I'm not saying Saul didn't existed, I say we have no proof he did.
You have to remeber that, in the old times, religion was used for political reasons much more than now, much more than even Huckabee would ever dream. For example, kings were anoited by the Pope, because they were supposed to be choosen by God to rule over their countries. eligion was a mean to control people so the Church had to control the Bible; They choosed carefully which writings woul be canon and included in the Bible and which wouldn't. And refering to those who hadn't been considered canon was considered to be heresy. Anything barely related to religion that wasn't controled by the Church was banned. Joan of Arch was burned at stake because she said she heard angels' voices ; The Church said that if god o Angel had something to tell to mortals, they would tell it to the Pope, no to some random teenage peasant girl.
The Bible is a spiritual book. You can believe what's in it if you want or you can not belive it. It's not an History book, nor a science book, you can't use the Bible as proof to bas a scientific or an historical claim, as you would do with writing from Pythagoras or Pliny the Elder.