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Was running a test using Backfire (BF) with the Heartbreaker (HB) set 4 piece bonus.
In the firing range AND in other activities, the 4-peice bonus breaks, and does not apply to the BF, nor any other weapons regardless of switching them out with something else (either through changing that slot's weapon, or using a different weapon slot).
HB 4-piece will not work with any weapon after BF breaks it. Using the Pulse skill does nothing besides pulse the targets (same as with any other armor loadout).