We derive a novel uplink-downlink duality principle for optimal joint precoding design under per-transmitter power and information constraints in fading channels. The information constraints model limited sharing of channel state information and data bearing signals across the transmitters. The main application is to cell-free networks, where each access point (AP) must typically satisfy an individual power constraint and form its transmit signal using limited cooperation capabilities. Our duality principle applies to ergodic achievable rates given by the popular hardening bound, and it can be interpreted as a nontrivial generalization of a previous result by Yu and Lan for deterministic channels. This generalization allows us to study involved information constraints going beyond the simple case of cluster-wise centralized precoding covered by previous techniques. Specifically, we show that the optimal joint precoders are, in general, given by an extension of the recently developed team minimum mean-square error method. As a particular yet practical example, we then solve the problem of optimal local precoding design in user-centric cell-free massive MIMO networks subject to per-AP power constraints.