We ask Allaah to grant your father a good end. The one who does righteous deeds during his life deserves to be honoured. This man has done well as he strove to fulfil his duties and avoid things that are forbidden. There are glad tidings for him and to others if they die as they lived.
We would point out that his making his children pay zakaah on their wealth whether it was a little or a lot, and even if the full year had not yet passed, may mean that he made them give charity, not the zakaah that is enjoined in Islam, because zakaah is only due on wealth when it reaches the minimum threshold (nisaab) and one year has passed. We ask Allaah to reward him for his intention, and to reward his children for what they have done.
Forgetfulness does not mean that the obligation of paying zakaah on his wealth is waived, because the obligation of zakaah is not subject to a person being sound of mind. Hence zakaah is required of young children and the insane. See question no. 75307.
What you have to do is to pay zakaah from his wealth on his behalf. You do not have to pay zakaah on the money he receives every month unless one full year has passed since he acquired it. It is difficult to work it out every month, so the easiest way to deal with such a case is to look at when his wealth first reached the nisaab, then calculate one year. When the year has passed, pay zakaah on all that he has, even the income from the last month. Then the zakaah on the first month will have been paid when the year is complete, and the zakaah on the following months will have been paid in advance, and there is nothing wrong with paying zakaah in advance.
See the answer to question no. 26113 for information on how to pay zakaah on a monthly income.
And Allaah knows best.