Is zakat obligatory on shares and cash balances (profits/distributions) in investment portfolios, and is it to be paid for one year upon liquidation or for all past years, given the lack of knowledge regarding the number of investment years and the amount of previous cash balances?

Zakat (definition) is obligatory on shares purchased for the purpose of sale, and their market value is the basis for Zakat calculation. As for shares held to benefit from their dividends, Zakat is only obligatory on the dividends, unless their assets are among those subject to Zakat by themselves (their intrinsic value), or if they include cash, in which case Zakat is obligatory on them. If the company pays Zakat on the shares with the shareholders' knowledge, then there is no Zakat due from the shareholders.

As for the cash balance in an investment account, Zakat is obligatory on the principal amount and its profit in Islamic banks, and on the principal amount only in interest-based (riba) banks. Zakat must be paid on this balance and the shares for all past years, if the Zakat payer's wealth reached the nisab (definition). Heirs must pay Zakat from the deceased's estate, as it is a debt that takes precedence over the division of the inheritance. If there is no certainty that the deceased did not pay Zakat, then the heirs are not obliged to pay it on his behalf, because the original principle is the absolution of liability. However, they must strive to estimate the Zakat due.