The attribution recorded for this path, the letter Tzaddi, the sign Aquarius, the trump of the Star, is the Golden Dawn's, and it is the one most modern sources give. There is a well-known challenge to it, and it comes from inside the tradition.
The Book of the Law, received by Crowley in 1904, states at chapter I verse 57: "Tzaddi is not the Star." Four words, no explanation, in a text its recipient regarded as not alterable.
Crowley did not know what to do with it for roughly twenty years. In The Book of Thoth he set out the solution he eventually adopted: the Star trump moves from Tzaddi and Aquarius to Heh and Aries, and the Emperor moves from Heh and Aries to Tzaddi and Aquarius. The two trumps exchange places, and the letters and signs stay where they are on the Tree.
His justification was that the exchange is symmetrical with one already accepted. The Golden Dawn had itself swapped Strength and Justice relative to the older printed tarot order, so that Strength takes Teth and Leo and Justice takes Lamed and Libra. Crowley pointed out that his Emperor and Star exchange is the same operation performed on a different pair, and that the two swaps sit symmetrically about the middle of the sequence. He also read Tzaddi, the fishhook, as better suited to the Emperor than to the Star.
Whether this follows from the verse is a matter on which Thelemites disagree, and it has been argued since. The verse says what Tzaddi is not; it does not say what it is, and the identification of the replacement is Crowley's inference. Practitioners in the Golden Dawn line, and those working with the older decks, have generally not adopted the change. Those working from the Thoth deck generally have, because that deck is built on it.
The material recorded here follows the Golden Dawn arrangement throughout, with the Emperor on the fifteenth path and the Star on this one. That is a choice between two documented systems rather than a neutral statement, and a reader comparing this against a Thelemic source will find these two trumps transposed and nothing else moved.
Both systems agree on the Strength and Justice swap. The disagreement is confined to one pair.