It's simple: You turn in the weapon and armor cores then a weapon or armor piece shows up on the screen like when it drops in a raid/nightfall etc. I did it and got the PoE sniper rifle. It's on my lvl 33 Warlock if you want to check it out. I was more hoping for an armor piece so he could be 34 (using an Etheric light) but I'll take the sniper too.