system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Wars] How did Kylo Ren recognize Anakin's original lightsaber?

The weapon was in it's prime two generations before him. And lost. How would he know that was Anakin's weapon?
gpt
Kylo has a rather strong obsession with Anakin/Vader, and it's not like it's a secret what his weapon looked like.  He also has the skills necessary to find and acquire Vader's helmet.  
I'd frankly be more surprised if he didn't know what it looked like.