Kylo kept his grandfather's helmet as a keepsake in that film, though it is nowhere to be seen in Star Wars: The Last Jedi. New information reveals what happened to Vader's helmet, and whether or not Kylo still has it in his possession.
In the Star Wars: The Last Jedi - The Visual Dictionary by Pablo Hidalgo, an entry on Kylo Ren offers new details about the character's personal headquarters. It reveals that he moved back in with his stepdad (AKA Supreme Leader Snoke) after being rescued from the destruction of the Starkiller Base.
But even though he's taken up residence on the Supremacy Star Destroyer, he has not transferred all of his belongings — including that important Sith relic.
"Rescued from the Starkiller disaster, Kylo returns to his quarters aboard the Supremacy, Supreme Leader Snoke's vast flagship. Here, Kylo's isolation allows him to meditate on the Force. He has left Darth Vader's charred helmet aboard the Finalizer, perhaps not ready to face that visage until he recovers from his failure."
This tidbit goes to show that for how much Kylo Ren attempts to be independent and do things his own way, he will always be influenced by the specter of his powerful grandfather. He attempts to maintain the perception that he has a strong and resolute will, yet cannot come to terms with the legacy of his own past without using it as a measuring stick.
Though the Finalizer is still roaming around in space, it remains to be seen if we will get to see Vader's helmet once again in the Star Wars saga. Kylo seems to have turned over a new leaf as the Supreme Leader of the First Order.
But does that mean he's done pleading and conversing with his grandpa's severed head? Maybe we'll find out in Episode IX.
For now, Star Wars: The Last Jedi is now playing in theaters everywhere.