In order to get this unique alien weapon in Far Cry 5, you have to find Larry and complete his side quests.
First you have to complete the Free Larry side quest. You can find Larry at the Parker Laboratories in John's Region, west of Fall's End. Where he trapped in an electrified cell. To free him you have to follow the blue cables on the ground to reach the respective generators.
You can stop these generators with a simple key command. The first generator you can find on the porch of the trailer, the second one is behind the house and the third one can be found north of the house at a small cubbyhole. After you disable them, return to Larry and speak to him. Larry likes to run away in the middle of a conversation. Stay on his heels so he can really tell you everything and start the next mission The Hero's Journey.
To get the aliens gun to your hand you have to complete Larry’ three quests. First, you have to tear down five satellite dishes for Larry, which are marked on the map. Before you start the quest, you should unlock the grappling hook, otherwise you will not reach the bowls. Of course some opponents are waiting for you here and also you have to take care of the enemies at Larry's house as soon as you get out of the helicopter and the first hurdle is done.
Next, Larry is targeting four alien objects, which you'll also see on the map. You can find them all in the area of the crop circle at Larry. For one of them you have to climb a silo, which you can either do with a helicopter or climb up from the inside.
Lastly, Larry asks you to go to the substation. Of course, you have to take car several opponents when you reach the goal marker. After that, you can start by bridging. The triggered alarm is part of the quest. Just hurry up while rerouting the transformers, and at best have a companion with you to keep rid of annoying enemies.
If you did that too, return to Larry and he'll ask you to press a button. Do this and watch what happens. Then you can take the unique alien gun and will also receive $ 1,600. The weapon is in the middle of the experiment field, where you first met Larry.