Moses definitely did not write the Pentateuch
I've casually studied the Documentary Hypothesis, its nuanced views (such as whether J and E should be treated as separate, or whether P is pre-exilic, post-exilic, or both), and competing theories (like the Fragmentary Hypothesis as suggested by Whybray). But generally in scholarship Mosaic authorship of the Pentateuch is not a good theory. It's a tradition, possibly originating in 2nd Temple Judaism, and has no support from the Pentateuch itself. The evidence from the Pentateuch, on many grounds, is actually against Mosaic authorship. There's a plethora of consilient evidence from many disciplines--linguistic, historical, etc.--that undercut Mosaic authorship. The Pentateuch is demonstrably post-Mosaic (filled with anachronisms), contradictory in many respects, and interspersed with confused traditions. There's little doubt that Moses did not write the Pentateuch.
Thanks,
Eric