Most scholars agree that the following story, told by the Jewish historian Flavius Josephus in his Jewish antiquities 11.317-345, is not true. One argument is that Alexander is shown a book that was not yet written. Another argument is that the story is a bit too good to be true: the Samarians, the eternal rivals of the Jews, blacken the Jews and get permission to build a temple of their own, Alexander visits Jerusalem, understands that he owes everything to the God of the Jews, allows them the privilege to live according to their ancestral customs and behaves rather unkind towards the Samarians. If a Jew in the second century BCE were to invent a story, he would write something along these lines.
On closer inspection, however, we may notice some odd details. In the first place, the Samaritans are allowed to keep their temple: not exactly something a Jew would invent, and in fact a plausible punishment for the Jewish refusal to send soldiers. In the second place, in fact, Alexander gives the Jews no privileges at all: everything he grants the Jews, had already been granted to them by the Persian kings. This was Alexander’s usual policy.
In the third place, the idea that Alexander had had a vision in which the God of the Jews played an important role is just too incredible to be invented: everyone knew that Alexander claimed to be the son of the Egyptian god Ammon. Nobody would invent a special link to the Jewish God. The easiest explanation is that Alexander did indeed sacrifice to the God of the Jews.
Another aspect that deserves to be mentioned is Alexander’s demand for auxiliaries and the presents the Jews formerly had sent to the Persian government. This matches the demand made by Alexander to Darius that he would address him as the master of the Persian possessions
The following translation was made by William Whiston (Ancient-Warfare)
So when Alexander besieged Tyre, he sent an epistle to the Jewish high-priest, to send him some auxiliaries, and to supply his army with provisions (1); and that what presents he formerly sent to Darius, he would now send to him, and choose the friendship of the Macedonians, and that he should never repent of so doing. But the high-priest answered the messengers, that he had given his oath to Darius not to bear arms against him; and he said that he would not transgress this while Darius was in the land of the living. Upon hearing this answer, Alexander was very angry; and though he determined not to leave Tyre, which was just ready to be taken, yet as soon as he had taken it, he threatened that he would make an expedition against the Jewish high-priest, and through him teach all men to whom they must keep their oaths. So when he had, with a good deal of pains during the siege, taken Tyre, and had settled its affairs, he came to the city of Gaza, and besieged both the city and him that was governor of the garrison, whose name was Babemeses.(2)
But the Samarian leader Sanballat thought he had now gotten a proper opportunity to make his attempt, so he renounced Darius, and taking with him seven thousand of his own subjects, he came to Alexander; and finding him beginning the siege of Tyre, he said to him, that he delivered up to him these men, who came out of places under his dominion, and did gladly accept of him for his lord instead of Darius. So when Alexander had received him kindly, Sanballat took courage, and spoke to him about his present affair. He told him that he had a son-in-law, Manasseh, who was brother to the high-priest Jaddus; and that there were many others of his own nation, now with him, that were desirous to have a temple in the places subject to him; that it would be for the king’s advantage to have the strength of the Jews divided into two parts, lest when the nation is of one mind, and united, upon any attempt for innovation, it prove troublesome to kings, as it had formerly proved to the kings of Assyria. Whereupon Alexander gave Sanballat leave so to do, who used the utmost diligence, and built the temple, and made Manasseh the priest, and deemed it a great reward that his daughter’s children should have that dignity; but when the seven months of the siege of Tyre were over, and the two months of the siege of Gaza, Sanballat died.
Now Alexander, when he had taken Gaza, made haste to go up to Jerusalem; and Jaddus the high-priest, when he heard that, was in an agony, and under terror, as not knowing how he should meet the Macedonians, since the king was displeased at his foregoing disobedience. He therefore ordained that the people should make supplications, and should join with him in offering sacrifice to God, whom he besought to protect that nation, and to deliver them from the perils that were coming upon them; whereupon God warned him in a dream, which came upon him after he had offered sacrifice, that he should take courage, and adorn the city, and open the gates; that the rest should appear in white garments, but that he and the priests should meet the king in the habits proper to their order, without the dread of any ill consequences, which the providence of God would prevent. Upon which, when he rose from his sleep, he greatly rejoiced, and declared to all the warning he had received from God. According to which dream he acted entirely, and so waited for the coming of the king.
And when Jaddus understood that Alexander was not far from the city, he went out in procession, with the priests and the multitude of the citizens. The procession was venerable, and the manner of it different from that of other nations. It reached to a place called Sapha, which name, translated into Greek, signifies a prospect, for you have thence a prospect both of Jerusalem and of the temple. And when the Phoenicians and the Samarians that followed him thought they should have liberty to plunder the city, and torment the high-priest to death, which the king’s displeasure fairly promised them, the very reverse of it happened; for Alexander, when he saw the multitude at a distance, in white garments, while the priests stood clothed with fine linen, and the high-priest in purple and scarlet clothing, with his mitre on his head, having the golden plate whereon the name of God was engraved, he approached by himself, and adored that name, and first saluted the high-priest.