All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The best action which a live person could do for his deceased relative is to give charity on his/her behalf, i.e. donating while intending the reward for the deceased.
'Aa'ishah narrated that a man came to the Prophet and said: "My mother died suddenly and I think that if she were able to speak, she would have given charity. May I give charity on her behalf? He replied, "Yes! Give charity on her behalf." [Al-Bukhari and Muslim]
It is also confirmed that Sa'd Ibn 'Ubaadah asked the Prophet if he can give charity on behalf of his dead mother and he permitted him to do so. [Al-Bukhari]
Indeed the scholars agreed in a consensus that charity and supplicating Allah to forgive the dead, reaches them. Ibn Al-Mubaarak said: “There is no difference of opinion that the reward of giving in charity on behalf of the dead reaches them."
Allah Knows best.