Which organelle synthesizes glycogen phosphorylase and why? I know that glycogen phosphorylase is not synthesized in the rough endoplasmic reticulum of liver cells, unlike many other proteins such as insulin receptor, lysosomal enzyme and serum albumin. I would like to know the organelle where glycogen phosphorylase is made and why it is made there.

Protein translation occurs via ribosomes bound to strands of messenger RNA in the cytoplasm; these structures are called polysomes but don't have a membrane surrounding them so you might not want to call them organelles. Polysomes making proteins destined for secretion, for the plasma membrane, or for some organelles (like your examples) are directed to the endoplasmic reticulum via a signal peptide typically near the beginning of the translated sequence. The combination of polysomes and endoplasmic reticulum is what is called rough endoplasmic reticulum. See this Wikipedia page for a more complete explanation of how particular proteins are targeted to their correct locations.