Falk claimed to possess thaumaturgic powers and to be able to discover hidden treasure. Archenholz (England und Italien, I. 249) recounts certain marvels which he had seen performed by Falk in Brunswick and which he attributes to a special knowledge of chemistry. In Westphalia at one time Falk was sentenced to be burned as a sorcerer, but escaped to England. Here he was received with hospitality and rapidly gained fame as a Cabalist and worker of miracles. Many stories of his powers were current. He would cause a small taper to remain alight for weeks; an incantation would fill his cellar with coal; plate left with a pawnbroker would glide back into his house. When a fire threatened to destroy the Great Synagogue, he averted the disaster by writing four Hebrew letters on the pillars of the door.[482] [Obviously the Tetragrammaton.]

On his arrival in London in 1742 Falk appeared to be without means, but soon after he was seen to be in possession of considerable wealth, living in a comfortable house in Wellclose Square, where he had his private synagogue, whilst gold and silver plate adorned his table. His Journal, still preserved in the library of the United Synagogue, contains references to "mysterious journeyings" to and from Epping Forest, to meetings, a meeting-chamber in the forest, and chests of gold there buried. It was said that on one occasion when he was driving thither along Whitechapel Road, a back wheel of his carriage came off, which alarmed the coachman, but Falk ordered him to drive on and the wheel followed the carriage all the way to the forest.

The stories of Falk's miraculous powers are too numerous to relate here, but a letter written by an enthusiastic Jewish admirer, Sussman Shesnowzi, to his son in Poland will serve to show the reputation he enjoyed:

Hear, my beloved son, of the marvellous gifts entrusted to a son of man, who verily is not a man, a light of the captivity ... a holy light, a saintly man ... who dwells at present in the great city of London. Albeit I could not fully understand him on account of his volubility and his speaking as an inhabitant of Jerusalem.... His chamber is lighted by silver candlesticks on the walls, with a central eight-branched lamp made of pure silver of beaten work. And albeit it contained oil to burn a day and a night it remained enkindled for three weeks. On one occasion he abode in seclusion in his house for six weeks without meat and drink. When at the conclusion of this period ten persons were summoned to enter, they found him seated on a sort of throne, his head covered with a golden turban, a golden chain round his neck with a pendant silver star on which sacred names were inscribed. Verily this man stands alone in his generation by reason of his knowledge of holy mysteries. I cannot recount to you all the wonders he accomplishes. I am grateful, in that I am found worthy to be received among those who dwell within the shadow of his wisdom.... I know that many will believe my words, but others, who do not occupy themselves with mysteries, will laugh thereat. Therefore, my son, be very circumspect, and show this only to wise and discreet men. For here in London this master has not been disclosed to anyone who does not belong to our Brotherhood.

The esteem in which Falk was held by the Jewish community, including the Chief Rabbi and the Rabbi of the new Synagogue, appears to have roused the resentment of his co-religionist Emden, who denounced him as a follower of the false Messiah and an exploiter of Christian credulity.

Falk [he wrote in a letter to Poland] had made his position by his pretence to be an adept in practical Cabala, by which means he professed to be able to discover hidden treasures; by his pretensions he had entrapped a wealthy captain whose fortune he had cheated him out of, so that he was reduced to depending on the Rabbi's charity, and yet, despite this, wealthy Christians spend their money on him, whilst Falk spends his bounty on the men of his Brotherhood so that they may spread his fame.

In general Falk appears to have displayed extreme caution in his relations with Christian seekers after occult knowledge, for the Jewish Encyclopædia goes on to say: "Archenholz mentions a royal prince who applied to Falk in his quest for the philosopher's stone, but was denied admittance." Nevertheless Hayyum Azulai mentions (Ma'gal Tob, p. 13b):

That when in Paris in 1778 he was told by the Marchesa de Crona that the Ba'al Shem of London had taught her the Cabala. Falk seems also to have been on intimate terms with that strange adventurer Baron Theodor de Neuhoff.... Falk's principal friends were the London bankers Aaron Goldsmid and his son.[483] Pawnbroking and successful speculation enabled him to acquire a considerable fortune. He left large sums of money to charity, and the overseers of the United Synagogue in London still distribute annually certain payments left by him for the poor.

Nothing of all this would lead one to suppose that Falk could be regarded in the light of a black magician; it is therefore surprising to find Dr. Adler observing that a horrible account of a Jewish Cabalist in The Gentleman's Magazine for September 1762 "obviously refers to Dr. Falk, though his name is not mentioned."[484] This man is described as "a christened Jew and the biggest rogue and villain in all the world," who "had been imprisoned everywhere and banished out of all countries in Germany, and also sometimes publicly whipped, so that his back lost all the old skin, and became new again, and yet left never off from his villainies, but grew always worse." The writer goes on to relate that the Cabalist offered to teach him certain mysteries, but explained that before entering on any "experiments of the said godly mysteries, we must first avoid all churches and places of worshipping as unclean"; he then bound his initiate by a very strong oath and proceeded to tell him that he must steal a Hebrew Bible from a Protestant and also procure "one pound of blood out of the veins of an honest Protestant." The initiate thereupon robbed a Protestant of all his effects, but had himself bled of about three-quarters of a pound of blood, which he gave to the magician. He thus describes the ceremony that took place:

Then the next night about 11 o'clock, we both went into the garden of my own, and the cabalist put a cross, tainted with my blood, in each corner of the garden, and in the middle of the garden a threefold circle ... in the first circle were written all the names of God in Hebrew; in the second all the names of the angels; and in the third the first chapter of the holy Gospel of St. John, and it was all written with my blood.