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No, it will NOT work in a MR556. The MR 556 has a firing pin safety that cannot engage unless you have a taller hammer. There is a geissele trigger that made for MR556/HK 416. when you look at that hammer it is a little taller to release the firing pin safety.
This trigger will fit in the receiver. It will "click" for dry fire. However, if you try to actually shoot, it will not actually engage the firing pin and shoot anything.
Yes this will still work with a MR 556.