DNA sequences are undergoing frequent changes if there is no evolutionary pressure on them. The message would quickly be scrambled. They would have to encode it

DNA sequences are undergoing frequent changes if there is no evolutionary pressure on them. The message would quickly be scrambled. They would have to encode it into highly conserved gene sequences, i.e., completely reinvent life as we know it. The moon is a harsh environment and (like most places in the solar system) exposed to significant danger from meteorites over geological timescales.