If a person donates on behalf of a dead person from his own money, not from the wealth of the deceased person, will the reward reach the deceased?

Praise be to Allaah. 

There is nothing wrong with that, and the reward will reach the person
for whom it was intended, if that money is spent for a good purpose
such as charity, upholding ties of kinship, jihaad and good works that
will benefit the Muslims, such as a person giving charity on behalf
of his grandparents, even if they did not leave behind any money, or
on behalf of his friend. The deceased will benefit from that. And Allaah
knows best.