Is it permissible to recite Al-Fatiha for the soul of the deceased, and what is the evidence for that?

If a Muslim recites the Holy Quran and dedicates the reward of his recitation to a deceased person, the predominant view is that the reward reaches the deceased. The hadith "When a human being dies, all of his deeds are severed except for three..." means the severance of the reward of the deceased's own actions, not the actions of others.