Ask your father to ask his broker whether the brokerage has records of the purchases.
The exact purchase date isn't important. As long as the stocks were originally purchased more than a year before you sold them, the gain is long-term. You can always enter "Various" for the acquisition date if know they are all long-term. But the cost is important because it directly affects how much tax you will have to pay. You can look up historical stock prices to get a reasonable estimate of the original purchase price, but to do that you have to have at least a rough idea of when each stock was purchased.
