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

Praise
be to Allah

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.