The brown is dead matter but not an indication that the moss itself is dying. I would probably trim out most of the brown, using very sharp scissors (like nail scissors or plant scissors). Java Moss does this when moved to different water parameters, at least in my experience. I have had it react similarly from one tank to another. Watch the light, it does not like bright overhead lighting and is best under some floating plants. Dappled light works well. I would also use a liquid fertilizer as this is a new tank. JM can manage without down the road, though it won't hurt and may be necessary for other plants anyway.
Byron.