I did my entire quest as petra lvl 1 and got nothing. But my friend also did it as Petra lvl 6 and still got nothing. It might be a bug
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Usually the Lost and Found quest will take a day to pop up, so unless he's waited that long don't assume it's glitched yet.
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I waited a day for that quest, I had to kill 50 on 3 different places on the Dreadnaught. Yet when I went to turn it in, there was nothing but quest complete
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It sounds glitched then. I will complete the bounty asap and see what happens. Still, Bungie should clarify on what exactly the problem and solution is.