This work presents itself as the teaching of Rabbi Shimon bar Yochai, a second-century Galilean sage, recorded by his circle and hidden for a millennium. It appeared in Castile in the 1280s, circulated by Moses de Leon, who said he was copying from an ancient manuscript in his possession.
Gershom Scholem made the case that de Leon wrote it, and made it on internal evidence. The Aramaic is not the Aramaic of second-century Galilee; it is an artificial literary Aramaic constructed by someone whose working language was Hebrew, containing calques and errors that a native writer of the earlier dialect would not produce. The text shows knowledge of medieval Castilian conditions and of philosophical vocabulary that postdates its claimed period by a thousand years. Its geography of the Land of Israel is that of a man who has read about it rather than walked it. And no source before the 1280s quotes it or refers to it, which for a work of that scale and eventual authority is decisive.
There is also the anecdote, preserved by Isaac of Acre, who went looking for the ancient manuscript after de Leon's death and reported being told by the widow that no such manuscript existed and that her husband had written it himself. It is second-hand, transmitted through a chain, and Scholem did not rest the argument on it. It is corroborative rather than load-bearing, and it is the part everyone remembers.
Scholarship since has complicated the conclusion without reversing it. Yehuda Liebes argued that the work is better understood as the product of a circle of mystics around de Leon than of one hand, on the ground that the stylistic and doctrinal variation across its sections is greater than single authorship comfortably explains, and later manuscript scholarship has supported a picture of gradual accretion rather than a single act of composition. What is not seriously argued in the field is the traditional attribution, which the linguistic evidence rules out.
The book's standing in Judaism is not affected by any of it. It became the central text of Kabbalah, was printed as such, was treated by many communities as very nearly canonical, and shaped Jewish practice and theology for centuries. The question of who wrote it in the 1280s and the question of what it has meant since are separate questions, and only the first one has an answer of this kind.