Each of Charles Dickens’ novels stands alone: they do not form a series or shared “universe”. So we should not expect to find references or allusions from one of his novels to the others.
The equation in the question, of the first death-cast with the Artful Dodger, seems to be a deduction from this sentence:
“Like him? It’s himself, you know. The cast was made in Newgate, directly after he was taken down. You had a particular fancy for me, hadn’t you, Old Artful?” said Wemmick.
Charles Dickens (1861). Great Expectations, chapter 24. Project Gutenberg.
But “artful” is a word meaning “skilful, wily, cunning, crafty, deceitful” and so anyone with these attributes might be so described. Elsewhere in Great Expectations we find:
Sarah was too knowing to be outdone, and ambled round Georgiana with that artful slipperiness [chapter 11]
“Not but what he’s [Jaggers] artful, even in his defiance of them” [chapter 25]
“first he [Compeyson] swore me (being ever artful) on my own book” [chapter 42]
Even allowing for the possibility that Wemmick might be referring to the character from Oliver Twist, the different fates of the characters makes the equation extremely unlikely. The Artful Dodger was transported to Australia for theft:
“They’ve found the gentleman as owns the box; two or three more’s a coming to ’dentify him; and the Artful’s booked for a passage out,” replied Master Bates. “I must have a full suit of mourning, Fagin, and a hatband, to wisit him in, afore he sets out upon his travels. To think of Jack Dawkins—lummy Jack—the Dodger—the Artful Dodger—going abroad for a common twopenny-halfpenny sneeze-box! I never thought he’d a done it under a gold watch, chain, and seals, at the lowest. Oh, why didn’t he rob some rich old gentleman of all his walables, and go out as a gentleman, and not like a common prig, without no honour nor glory!”
Charles Dickens (1839). Oliver Twist, chapter 43. Project Gutenberg.
whereas Jaggers’ client in Great Expectations “murdered his master” and was hanged for it: Wemmick says in the quote above that the death-cast was made “directly after he was taken down” from the gallows.
Of the other death-cast, Wemmick says that this client forged wills (presumably to his own benefit), and probably murdered the testators too:
“Yes, he came to the same end; quite the natural end here, I assure you. He forged wills, this blade did, if he didn’t also put the supposed testators to sleep too.”
This does not correspond to the fate of Fagin in Oliver Twist. Although there is a subplot concerned with Mr. Leeford’s will, this is genuine and not forged; and Fagin is hanged for complicity in the murder of Nancy, who would not be described as a “testator”.