We derive a novel uplink-downlink duality principle for optimal joint precoding design under per-transmitter power and information constraints. 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 on the basis of possibly partial data and channel state information sharing. By measuring performance using the popular hardening inner bound on the ergodic capacity, we show that optimal joint precoders can be interpreted as optimal joint combiners on a dual uplink channel with properly designed transmit and noise powers, and that they can be obtained using a variation of the recently developed team minimum mean-square error method. We finally apply our results to the numerical evaluation of optimal centralized and local precoding in a typical user-centric cell-free network subject to per-AP power constraints.