Are we to understand that the sperm that unites with the woman's egg has no soul, based on the insufflation of the soul into the fetus after four months?

Both the sperm and the woman's ovum possess reproductive life that qualifies them for union and the formation of a fetus. When the soul is breathed into it, another life flows within it. Humans cannot encompass all the mysteries of pregnancy, for Allah alone knows what is in the wombs. Life has many forms, and every living creature has a life suited to it by the power of Allah, and Allah has made water the origin of every living thing.