Are the funds that the father distributed to his children and grandchildren during his lifetime, and which were deposited in the bank in the name of one of the sons, considered a legal inheritance after his death that must be distributed?

If a gift fulfills its legal conditions, such as the giver bestowing it not during a death-threatening illness, and the recipient taking possession of it during the giver's lifetime, then it is not to be divided among the heirs; because it has exited the possession of the giver. As for a gift given during a death-threatening illness, it takes the ruling of a will, and is not valid for the children. Rather, it reverts to the estate and is divided according to the legal inheritance distribution.