In a soft contact lens manufacturing process, an injection molding machine (IMM) produces many thermoplastic injection molded front curve (FC) and back curve (BC) mold parts, each of which mold parts is subsequently used only once to mold a single soft contact lens. An inlay station with alignment assemblies and transfer tubes provide for the precise transfer to and alignment of the FC and BC molds in pallets during their transfer from the IMM to pallets on an assembly line in a high speed automated commercial production operation. A rotatable FC transfer arm and a rotatable BC transfer arm transfer the FC and BC molds from the IMM machine to the pallets in an inlay station. The precisely aligned transfer is provided by two alignment rods of an alignment assembly which pass through two alignment apertures in the pallet and then pass through two alignment apertures in one of the FC or BC alignment arms.