Can you provide an actual quote by Pope John Paul II that states that life begins at conception?

Answer

Sure:

Some people try to justify abortion by claiming that the result of conception, at least up to a certain number of days, cannot yet be considered a personal human life. But in fact, “from the time that the ovum is fertilized, a life is begun that is neither that of the father nor the mother; it is rather the life of a new human being with his own growth.” (Evangelium Vitae 60, quoting Congregation for the Doctrine of the Faith, Declaration on Procured Abortion 12)