Final answer:
The molecule that transfers genetic instructions from DNA to the cytoplasm is messenger RNA (mRNA), which is synthesized during transcription and then guides protein assembly during translation.
Step-by-step explanation:
The molecule that copies the genetic instructions from DNA in the nucleus and carries them to the cytoplasm is RNA, more specifically, messenger RNA (mRNA). mRNA is a single-stranded nucleic acid that plays a crucial role in the synthesis of proteins.
During the process of transcription, mRNA is synthesized using a DNA strand as a template. This message is then transported out of the nucleus through the nuclear pores to the ribosomes in the cytoplasm or on the rough endoplasmic reticulum (RER). Once there, mRNA provides the sequence of bases that dictates the order of amino acids in a protein, which is assembled during the process of translation.