According to the basic principles of Shari`ah (Islamic law), a dead Muslim person may not be buried before offering Funeral Prayer for them. What you have just cited is no more than a hypothetical case. However, given that a Muslim is buried without offering Funeral Prayer for them, such Salah is to be offered for them at the grave. Moreover, leading Funeral Prayer is not limited to a certain Imam.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.