Thanks to DF, this was done quick, enjoy another one. 

6 BBY - Mustafar, Fortress Vader medical bay

A few days have gone by since Vader’s confrontation with Captain Rex and Cyron Klask on Crait. The Sith Lord was found by the Emperor and had now recovered from that duel, as he entered a medical room and saw a pair of medical droids gazing at the body of his secret Apprentice that was now dressed in a medical robe.

“Ah, Lord Vader! The Apprentice is regaining consciousness. What shall we do?” 

“Keep him restrained.”

The medical droid nodded, before Starkiller’s eyes snapped open and realized he was now strapped to an operating table, until he looked at his Master. " You!! You KILLED ME!!!!”

" No, Lord Starkiller. The Emperor thinks you're dead, but I salvaged your body and brought you here to be rebuilt. Now, your entire existence must be kept secret until my Master is dead. Is that understood, my Apprentice…?”

Starkiller sighed and looked at the bright light shining upon the operating table, then back at Vader with his eyes bearing a dark red glow. “Yes, Lord Vader…”

16 BBY - Ilum

Rex sits down in front of a wall, as he begins to tire. He has been wandering the surface of Ilum for hours, looking for a Kyber Crystal in order to construct his first Lightsaber, only to find that the Empire has mysteriously been turning the planet into a biomechanical nightmare and had to fight several Stormtroopers guarding the machinery.

But then, Rex turned his head and felt something calling to him from inside one of the caves.

Standing up, Rex slowly walked towards the cave and began to see a golden glow as he got closer towards the cave. Finally, he approached the place where he felt the Force calling to him and saw a yellow Kyber Crystal lodged into the walls of the cave.

Walking towards the Crystal, Rex managed to wedge it out of the cave wall and took a bag of metal parts out of a bag Ahsoka had given him prior to him arriving on Ilum and rested both them and the Kyber Crystal down on the icy ground and closed his eyes.

The Crystal and the parts began to float around Rex, before they mashed together into a Lightsaber hilt and Rex reopened his eyes, grabbing the hilt and ignited a yellow blade. After staring at his new weapon for sometime, Rex deactivated his Lightsaber and contacted Ahsoka over his comlink. “Commander Tano, I think I’ve found what I was looking for…”