Same Issue here. Picked up the research module from failsafe, and then got the specimen from the battleground, but there is no where to take it because there is no quest associated with the specimen.
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Once you have it you should get a 3 step chores list to complete, I got auto rifle kills, solar kills and making orbs, boring whatever it was. Then you can stuff the maguffin in a case with the other junk. Think you see failsafe after you collect the piece of junk.