Red Currants do very well in partial shade with heavy fruiting. I have had Red Currants in part sun, part shade for many, many years.

Currants will tolerate some shade but not wet soil. If area is covered with moss, it should be pretty wet constantly. I would create raised beds to improve the drenage and don't plant bushes too close to each other to improve air circulation and prevent mold on berries.
Yelena