If I had to guess, not only would you not keep the kill count, it wouldn't be a masterwork weapon either.
You could get another better devils, because you have had it before, but its a new better devils, so there is no kill count on it, and it wouldn't be a master worked better devils.
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No, that cant be. Because atm exotic masterwork still have their catalyst when you find a second one or build it form scratch out of vault. But the Killcount on a newly found exotic is ofc zero.
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Legendary weapons don't have catalysts. They are different. If you have a master worked better devils, and you get a new one. Unless it dropped as one, you will need 10 cores to make it one.