It puzzles him to have the country cousin clutch his arm and enquire whether that rough-looking customer coming out of a Chatham Square saloon is a dip, a yegg, a stall, a moll-buzzer, a Fagin, or a gun.
-- N.Y. Evening Post 25 Aug, 1910.

'Mollbuzzer' was Victorian era street slang for a pickpocket who steals from women (that is, one who buzzes molls). It was in much wider circulation than a modern American might assume, apparently a pickpocket might make a good living poaching on unsuspecting well-to-do ladies. Handbags may also present a sufficiently unique challenge to a pickpocket that specialization was important.

It should be noted that occasionally 'mollbuzzer' will be used to refer to a female pickpocket, rather than a pickpocket that preys on females. You will have to rely on context to determine which is intended.

Compare to Kirkbuzzer.