All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
In a shirkat al-‘inān partnership, the two partners pay zakāh according to the rules of jointly mixed wealth (zakāt al-khulṭah), such that zakāh is due from each partner in proportion to his share.
As for a muḍārabah partnership, the owner of the capital pays zakāh on both the capital and the profits that appear. The working partner, however, does not pay zakāh on his share of the profit until one lunar year has passed after the profits have been distributed, provided that his share reaches the niṣāb (Minimum amount liable for Zakah). This is because the working partner does not fully own his share of the profits until the division takes place, and therefore the zakāh year begins only from that point.
Accordingly, if the capital owner and the working partner mutually agreed to pay zakāh as though their arrangement were a shirkat al-‘inān, and later discovered that this was incorrect, then the working partner has the right to seek reimbursement from the capital owner for the amount he paid as zakāh on the latter’s share. This is because it became clear that the zakāh he discharged was in fact obligatory upon the capital owner.
It is stated in Asnā al-Maṭālib (Vol.1/P.349): “Branch issue: Zakāh may become obligatory in a partnership of mixed ownership. For example, if two people jointly own five camels and one of them pays the sheep due for zakāh, then he may seek reimbursement from the other for half of its value.”
However, if the working partner paid the zakāh voluntarily on his own initiative, without any prior agreement with the capital owner, then what he paid would count toward the zakāh due on his own other wealth—if he possessed other zakātable assets. Otherwise, it would be regarded as voluntary charity for which he will be rewarded.
In conclusion, the working partner may seek reimbursement from the capital owner or his heirs—provided he can establish proof of the agreement, or the heirs acknowledge it—if the zakāh was paid based on mutual agreement between the two parties. But if he paid it independently without prior agreement, then he has no right to claim anything from them. And Allah, the Most High, knows best.