Is it permissible to sponsor an orphan and dedicate the reward for yourself and your deceased parents, or is it a condition that your father must have sponsored him before his death?

The reward for charity reaches the deceased and benefits them, by the consensus of the imams. Sponsoring an orphan is among the best forms of charity. It is permissible for a Muslim to dedicate the reward of their good deed, including sponsoring an orphan, to themselves and their deceased parents. The deceased benefits from this, and it is not a condition for the reward to reach them that the deceased had sponsored an orphan before their death.