Their father left them a business venture, and they agreed to divide its income by rotation, so that every year two of them will take that year’s income

Praise be to Allah.

If the heirs are partners in a commercial venture or the like, such as if they are partners in some product that is sold, such as if their father left them a store where they sell some products, or a factory and they sell what it produces, and the like, in which they can share out the income, and its profit varies from one time to another or from one year to another, then it is not valid to distribute the income by rotation in such a way that two of them share its income every year. That is because there is a variation – as is pointed out in the question. So there may be a profit one year, and a loss or reduced profit in another year. The partners have no right to share out the profit in this manner, such as if one of them says: I will take the profit of this trip, and you can take the profit of the following trip, or I will take the profit of this month or year, and you can take the profit of the following month or year.

Ibn Muflih (may Allah have mercy on him) said in al-Furoo‘ (7/114): If they stipulate that they both, or one of them, will have a percentage of the profit that is unknown, or that is like what So-and-so stipulated for So-and-so, or a known percentage with one dirham more or one dirham less, or earning half of that amount, or a set amount, or the profit of one trip, or of one year, or the matter was never discussed, then the (partnership) deal is invalid. End quote.

Al-Bahooti said in Kashshaaf al-Qinaa‘ (3/499), regarding the ‘inaan partnership: If they stipulated that one of them will have the profit of one of the two garments, or the profit of one of the two trips, or the profit earned through the trade of a particular month or a particular year, that is not valid, because he may make a profit in that particular trip and not others, or vice versa, so that only one of them will make a profit, to the exclusion of the other, and that is contrary to the concept of partnership. End quote.

Based on that, in a partnership such as this, all partners must share the income of each year, so they must divide it among themselves.

And Allah knows best.