Imposter is more of standalone episode and itself borrowed from an element of Dicken's Oliver Twist.
The Greenwood family are well to do but haunted by tragedy. Some years earlier they lost their little boy on a visit to the fair.
Fagin sees an opportunity for Dodger to return as the lost boy. Sykes can then later rob the place.
So Dodger has his hair dyed and a birthmark painted on his face. A backstory of being taken by pirates. It might be enough to fool the family.
Dodger likes the good life with the Greenwoods. A family that adores him and he cannot bear to see them being robbed.
However a portrait painter has his doubts about the impostor.
There is a scene where Dodger realises the enormity of the task before him. As he learns from the Greenwoods the various skills and things their lost child did. I think it was a homage to an episode from Blackadder II.