The problem is that coal plants are sprinkled with a whole bunch of radioactive fly ash, and normal radiation level for a coal plant would violate the hell out of regulations for a nuclear plant.
What makes an object unique then is the specific configuration of the particles that make up that object. This configuration is a form of information.
Fortunately, we already know how to transmit information at the speed of light; no new physics required. This then reduces the problem to transporting the ‘printer’. No generation ship required. You need something that harvests particles locally and can receive a stream of data with what to print. You can bootstrap this, send a tiny particle harvester/printer that can print a slightly larger printer, etc.