All perfect prays be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
One who abandoned prayer, fast, and alms has committed a great sin, and is in great danger before Allah, The Almighty, since these are the pillars of Islam, and whoever upholds them upholds Islam, but whoever abandons them undermines Islam.
However, since Allah`s mercy has encompassed everything, making supplication as well as doing good deeds on behalf of that person may benefit him, with Allah`s permission. In addition, prayer can`t be made up on behalf of the deceased because it is Allah`s right on every Muslim, and there is no text in Sharia allowing such a thing, unlike fasting and Hajj. However, it is preferable to make as much supplication for the deceased as possible and to give charity on his behalf as well. This way, Allah, The Almighty, might forgive him, or charity could reduce his sin. As regards alms or Zakat, a person remains liable for it, even after his death, because it is an established right of the poor. Not only that, but payment of the Zakat due on the deceased takes precedence over settling his debts. Ash-Shirbini said: "If a Muslim passed away while liable for Zakat and debts, and his estate didn`t cover both, then Zakat must be paid first."{Moghni Al-Mohtajj, 2/126}.
On the other hand, it is permissible to observe fast and perform Hajj on behalf of the deceased. As for Hajj, the expenses are to be covered from the deceased`s estate. This is reflected in the following narration: a woman from the tribe of Juhaina came to the Prophet (PBUH) and said, "My mother had vowed to perform Hajj but she died before performing it. May I perform Hajj on my mother's behalf?" The Prophet (PBUH) replied, "Perform Hajj on her behalf. Had there been a debt on your mother, would you have paid it or not? So, pay Allah's debt as He has more right to be paid."{Bukhari}.
Furthermore, it is permissible for the heirs to make up for the obligatory fast missed by the deceased. They can either feed one poor person for each missed day, or fast those days on his behalf. Prophet Mohammad(PBUH) said: "Whoever dies while he still has some fasts to make up (of the days of Ramadan), then his heir (any of them) should fast on his behalf."{Bukhari}. The Prophet also said: ‘Whoever dies owing the fasts of a month, one poor person should be fed on his behalf for each day.”{At-Tirmizi}.
As regards the inherited money, it is considered lawful and there is no harm on the heirs to take it. However, amounts resulting from that money being employed in usurious transactions are unlawful, and must be donated to the poor and needy. And Allah knows best.