Final answer:
The Golgi apparatus is responsible for packaging proteins that are to be exported through the cell membrane, functioning as part of the endomembrane system alongside the nucleus, ER, and other cellular components.
Step-by-step explanation:
The cellular component that packages proteins for export through the cell membrane is the Golgi apparatus. This organelle manipulates products from the rough endoplasmic reticulum (ER) and produces organelles such as lysosomes. Proteins and other products from the ER are sent to the Golgi apparatus, which then organizes, modifies, packages, and tags them for transport to other areas of the cell or for export outside of the cell through exocytosis. The endomembrane system, of which the Golgi is a part, works closely with the nucleus, rough ER, and other components to ensure that proteins are properly synthesized, processed, and transported within the cell.