star wars - How can Kylo Ren recognize this item?

During the last part of The Force Awakens, Kylo Ren faces Finn in a snowy forest on Starkiller base. Finn lights up Luke's lightsaber to fight against Kylo Ren. Kylo immediately says something like:

That lightsaber, it belongs to me!

My question then is

How can Kylo Ren possibly know that this lightsaber was Luke's and Anakin's? Did Maz Kanata show him before the events of the Force Awakens? Did he feel through the Force that it was his

old grandfather's saber?

Did he not know and this line was just a bit confusing?

Answer

There are a couple ways Kylo Ren would know about and recognize the Skywalker lightsaber:

1. 
   

   Information on Anakin's lightsaber was likely communicated to Kylo Ren by Luke himself. Kylo Ren was initially trained by his uncle, Luke Skywalker. Since they trained together, and are family, Luke probably told him about Obi-Wan giving him Anakin's second lightsaber. As far as recognizing it on sight, Luke could have shown him recordings or diagrams from R2-D2's memory banks or even sketches to help illustrate how to make a lightsaber.

   
   


2. 
   

   Kylo Ren appears to be obsessed with Vader. He even tracked down Vader's burnt helmet. If he's willing to hunt down Vader's burnt helmet, he'd probably be interested in other artifacts connected to Vader. While hunting for anything connected to Vader, he would have learned about Anakin's lightsaber. Images of the lightsaber were probably on file in old Imperial or Republic records.

   
   

_{It could also be that Kylo Ren recognized the lightsaber for reasons that are purposefully left unexplained, meaning the forthcoming films will address why Kylo Ren could recognize the lightsaber and why he said it was his.}