They do!
(To make my life easier, Faller Anabel will be referred to as Anabel J. and non-Faller Anabel will be referred to as Anabel B.-F.) Anabel J. was the first one to become aware of her other self, mainly since she was interested in the possibility once she found out what being a Faller entailed. She didn’t go further than learning the basics though, pretty much just the equivalent of a google search. She didn’t want to pry into the life of this world’s Anabel since it just seemed weird to. She was the ‘intruder’ after all. Anabel J. didn’t pay too much attention to what her other self was doing until she met Layla when the girl was assigned to work under her as a rookie. The resemblance between them was undeniable, and Anabel is convinced her superiors paired the two of them on purpose just to mess with them. Obviously, Layla wanted to know why her superior was a doppelganger of her mother, so Anabel J. explained the whole situation. This eventually led to Anabel B.-F. finding out about Anabel J.’s existence, mainly due to Layla’s influence. The two of them consider each other friends, but also the whole ‘looking identical down to their names’ thing is a bit off-putting for the two of them. The only one who regularly interacts with both is Layla and she considers Anabel J. to be something of an aunt, while Anabel J. herself thinks of Layla a bit like a daughter (which she…. technically is). So, long story short, they do know of each other and are on friendly terms, but don’t really interact that much since both find the idea of having a double a bit weird.