In the case of business partnerships, it is not stipulated that the shares invested by the partners or their shares of the profits should be equal

Firstly:

If the partnership is established with investment of wealth by both partners, and the work is done by both of them or by someone whom they appoint, then this is called an ‘anaan partnership.

Ibn Qudaamah (may Allah have mercy on him) said:

… The second category is when two people form a partnership, each putting effort and wealth into it. This is the third type of partnership and it is called an ‘anaan partnership. What this means is that two men put their wealth into a partnership and both work in the business venture, and the profit is shared between them.

End quote from al-Mughni (5/11).

Secondly:

In the case of an ‘anaan partnership – according to the more correct view – it is not stipulated that both partners should put in an equal amount of wealth. If one of them invests ten thousand and the other invests twenty thousand, or if one puts in sixty percent and the other puts in forty percent, the partnership is sound and valid, because the basic principle with regard to business dealings is that they are permissible, and in this case there is nothing to disallow it.

Ibn Qudaamah (may Allah have mercy on him) said: It is not stipulated that the amount contributed by each party should be the same. This was the view of al-Hasan, ash-Sha‘bi, an-Nakha‘i, ash-Shaafa‘i, Is-haaq and as-haab ar-ra’y. Some of the companions of ash-Shaafa‘i stated that the shares should be equal.

End quote from al-Mughni (5/13)

Al-Bahooti (may Allah have mercy on him) said: If they become partners in property in a case in which it is not clear which part of it belongs to whom, such as if they inherit it or it was given to them as a gift, and they do not know the exact size of the property in question (so they decided to be partners), the partnership is valid, provided that they know the percentage that each of them holds in the partnership, whether it is one half, one quarter and the like, because in that case there is no ambiguity.

End quote from Kashshaaf al-Qinaa‘ (3/498).

Thirdly:

The specific share of profits between the partners depends on what the partners agreed to, not on the amount that each partner contributed. If one of them contributed forty thousand and the other contributed sixty thousand, but they agreed that the profits should be shared equally between them, or that one of them should take one third and the other should take two thirds, that is valid and sound. 

Ibn Muflih (may Allah have mercy on him) said in al-Furoo‘ (4/404): The profit of each partnership is to be shared according to what the partners agreed on, even if the shares of profit are different and the wealth they contributed was the same. End quote.

For more information, please see the answer to question no. 186407.

Fourthly:

It is stipulated that the percentage of profit of each partner must be known to each partner, whether it is one half or one quarter or one third and the like. If they form a business partnership and they agree that each of them should have half (of the profits), then the partnership is valid. But if they agree that one of the partners should have a share of the profits equal to one thousand dirhams, for example, and the rest should go to the other partner, this is not valid, because it is not known, and when it is not known it may lead to the entire profit going to one of them, in which case the other would receive no profit, and this is a kind of ambiguity.

Fifthly:

The scholars (may Allah have mercy on them) stated that one of the things that render a partnership invalid is the death of one of the two partners. So if two people form a business partnership, then one of them dies, the partnership between them is nullified, because the heirs have the right to their share of the estate.

Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (5/16):

Partnerships are a kind of permissible contract, but the partnership is nullified if one of the partners dies, becomes insane, or is deemed legally incompetent to handle wealth, or if the partnership is cancelled by either partner, because it is a permissible contract, therefore it is rendered invalid by these things, as is also applicable in the case of the appointment of one person to act on behalf of another (wakaalah). End quote.

If the partnership is nullified (because of the death of one of the partners), the heirs have the right to agree with the other partner to continue the partnership, either under the previous conditions or under new conditions. They also have the right to withdraw their share from the partnership.

And Allah knows best.