How is the profit share calculated in a partnership based on effort, where the proportions were not determined beforehand, and one of the partners has died, leaving heirs? And does the partner who exerted greater effort deserve a higher percentage of the profits?

A company in which the share of profit for each partner is not specified is a فاسدة (invalid/corrupt) partnership. Accordingly, if each partner has distinct capital, then each one of them is entitled to their capital and profit. However, if the capital is mixed, then each one of them is entitled to their capital and their share of the profit commensurate with their capital. If the partnership is based solely on labor, then the earned money is divided equally between them, and each takes half of the other's labor wage from their share.