Upon whom is the zakat due for my share of the merchandise – which was the result of a partnership between me and my brother – and which has now become his property, with the understanding that he will pay me its value over several years, while he trades with it during this period?

If you agree with someone to pay the price of goods in installments, then this amount becomes a debt owed to you by him, and it is subject to zakat (definition) as a debt. If the debtor is solvent, capable of repayment, and not a denier, then zakat on the debt is obligatory every year. It is permissible to delay it until it is collected, and then it is paid for all past years. However, if the debtor is procrastinating, denying, or insolvent, then zakat is not obligatory until the debt is collected. At that point, the calculation of the hawl (one lunar year) begins from the day of collection, and it is safer to pay zakat for one year upon its collection. As for the goods themselves, their zakat is obligatory upon your partner who bought them and they became his property.