Can You Give Zakat on Behalf of the Dead?
Question

My grandmother wanted to know if Zakat Al-Fitr of `Eid can be given in the name of a dead person, for e.g. her parents.
Praise be to Allah.Zakat Al-Fitr is obligatory for all Muslims, males and females, old and young, as stated by the Prophet (peace and blessings of Allah be upon him). 
Zakat Al-Fitr is only required from the living who are present at the time when it becomes due. 
The time when Zakat Al-Fitr becomes due is when the sun sets on the last day of Ramadan, because the Prophet (peace and blessings of Allah be upon him) called it Sadaqat Al-Fitr, and Fitr or breaking the fast of Ramadan comes when the sun sets on the night of Eid (i.e., the night before Eid). It is a purification for the fasting person from any idle or obscene speech, and the fast ends when the sun sets. 
If a person dies before the time it becomes obligatory, he does not have to pay this Zakah. If a person lives until the time when it becomes obligatory, then dies before paying it, then it should be paid on his behalf from his wealth because it is still a duty that he owes and becomes a debt that must be paid on his behalf. (See: Al-Majmu`, 6/84; Al-Mugni, 2/358; Al-Mawsu`ah Al-Fiqhiyyah, 23/341) 
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: 
“If a person dies before the sun sets on the night before `Eid, he does not have to pay Zakat Al-Fitr, because he died before it became obligatory.” (Fiqh Al-`Ibadat, p. 211) 
In conclusion, the deceased person is responsible for this if he died after the time when it became obligatory, which is sunset on the night before Eid. In that case it must be paid on his behalf.
 If he died before the time when it became obligatory – which appears to be the case in the question asked here – then this Zakah is not obligatory. 
If your grandmother gave charity such as food, money, etc. on his behalf, then it is charity given on his behalf and is not Zakat Al-Fitr. 
It is proven in more than one Hadith from the Prophet (peace and blessings of Allah be upon him) that charity given on behalf of the dead benefits them and the reward reaches them . 
And Allah knows best.