It is obligatory to recite Surah Al-Fatihah in the Funeral Prayer after the first Takbir which is Takbirat-ul-Ihram (saying: "Allahu Akbar [Allah is the Greatest]" upon starting Prayer). This is according to the general saying of the Prophet (peace be upon him):
Salah of anyone who does not recite Surat Al-Fatihah is invalid.
It was authentically reported that the Prophet (peace be upon him) used to recite it after the first Takbir. One should also ask Allah to confer peace and blessings upon the Prophet (peace be upon him) after the second Takbir. Supplicating to Allah for the dead person and others should be performed after the third Takbir. Then one should perform Taslim (salutation of peace ending the Prayer) after the fourth Takbir.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.