The most appropriate one-word substitution for the given group of words "A device that transmits written message from far off place" is "Telegraph."

1. Speedpost: Speedpost refers to a postal service that provides faster delivery of mail and packages compared to regular mail services. It is commonly used for express delivery or urgent shipments. However, it does not specifically relate to transmitting written messages from a far-off place.

2. Seismograph: A seismograph is a scientific instrument used to measure and record seismic waves or vibrations in the Earth's crust, primarily earthquakes. It is not related to transmitting written messages.

3. Telegraph: The telegraph is a device used for long-distance communication by sending coded electric signals over wires. It was one of the earliest forms of electrical communication, enabling the transmission of written messages from one location to another. The messages were encoded using Morse code, and the telegraph system revolutionized long-distance communication before the advent of telephones and the internet.

4. Telegram: A telegram is a written or printed message transmitted through telegraphy. It is a specific type of communication that utilizes the telegraph system to send and receive messages over long distances. Telegrams were widely used in the past, but their popularity has diminished with the rise of modern communication technologies.