Green’s Dictionary of Slang

a pickpocket.

1898		Binstead & Wells A Pink ’Un and a Pelican 88: I pushed my way out to where fresh air and the fob-divers were waiting.
1900		Sporting Times 24 Mar. 1/2: As old Fogo, the veteran fob-diver, dashed up a blind alley off Drury Lane, he ran into and nearly capsized a more youthful get-a-bit.