Placentally oxygenated blood passes via the umbilical vein into the fetus. Part of this blood bypasses the liver via the ductus venosus and goes to the inferior vena cava and then the heart. The rest passes through the liver before going to the IVC and the heart. After the now partially oxygenated blood enters the right heart, it is primarily shunted via the ductus arteriosus (and intracardiac shunts) away from the lungs and towards the aorta directly to the tissues and ultimately to the umbilical artery and the fetus for reoxygenation.
At birth (over the first days of life in healthy full-term babies), both the ductus venosus and the ductus arteriosus close allowing for the creation of the normal circulatory pattern of venous blood to the liver and the lungs.
Neonatologists cannulate both the umbilical vein and use it as a central line and the umbilical artery (there are normally 2 arteries and one vein) in sick babies and use them for monitoring.
In other words, both Acheiver and Kaplan are oversimplified explanations, although for a one sentence answer, Acheiver is closer to the truth.
OBP and the SDN neonatology service are here for you!