Is it permissible for one of the heirs to take the gold and pay its value to the other heirs by installments?

I.

If one of the heirs wants to take something from the estate and give the other heirs something in return for it, this is known as takharuj (inheritance settlement agreement).

It says in Al-Mawsu`at al-Fiqhiyyah (11/5): … In the case of a partnership, takharuj refers to an agreement whereby one partner exits the partnership by selling his share to another partner.

In Islamic terminology, takharuj refers to an inheritance settlement agreement, whereby one of the heirs excludes others from the estate in return for giving something of known value. End quote.

II.

If the inheritance settlement agreement has to do with one heir taking gold in return for cash, then the exchange must be done immediately after reaching the agreement, and it is prohibited to delay payment.

That is because in this case, the inheritance settlement agreement is like a transaction, or it is like an agreement that takes the form of buying and selling, and it is not permissible to sell gold for cash to be paid later.

In Al-Mawsu`at al-Fiqhiyyah (11/5), it says: The basic principle regarding inheritance settlement agreements is that it is an agreement between the heirs to exclude one of them from his share in return for his giving something, but it is regarded as being like a business transaction if what is given in return is something that is not part of the estate. And it is regarded as a transaction of share and exchange if what is given in return is part of the estate; or it may be a gift or waiving something, if what is given in return is of lower value than the allocated share. End quote.

It also says (11/7) about the conditions of inheritance settlement agreements: The exchange should be done immediately when what is exchanged is like currency for currency, such as an inheritance settlement agreement that involves exchanging gold for silver, and the same applies when exchanging any items that are susceptible to riba. This is a general guideline, but there may be differences in details, which we will discuss when we examine different forms of inheritance settlement agreements. End quote.

There is no difference of scholarly opinion regarding this scenario, because it is an exchange of currency for currency, which should be done immediately.

Some views of the jurists regarding that:

Al-Hasakfi said in Ad-Durr al-Mukhtar (p. 543): Chapter on inheritance settlement agreements: When the heirs exclude one of their number from part of the estate – whether it is an item or property – in return for giving him some money; or they exclude him from part of the estate – namely gold – in return for silver, or vice versa… All of that is valid, because it is an exchange of something for something of a different nature, whether they give him a little or a lot in exchange, but that is subject to the condition that the exchange be done immediately if it is exchanging currency for currency. End quote.

‘Ulaysh said in Minah al-Jalil (1/153): It is not permissible to make an agreement to exchange part of the estate for something that is not part of the estate, whether that involves gold or silver, a little or a lot, and whether the entire estate is available or not, because it is selling gold or silver or an item for gold or silver, which is riba al-fadl (usury of excess - exchange of the same type of commodity for an unequal amount of the same commodity), and it may also involve riba an-nasi’ah (the usury of delay, or interest on a deferred loan) if some or all of the estate is not available, even if it is an item, because the item comes under the same ruling as currency if it is added to currency [in a deal], except in the case of a settlement that includes an item that is not part of the estate, in which case it is permissible … End quote.

Al-Khatib ash-Sharbini said in Mughni al-Muhtaj, 3/162: If two parties agreed that debt owed by one of them will be paid with a different item, such as paying a debt owed in the form of silver in the form of gold, then the payment must be maid immediately after reaching this agreement, so as to avoid riba. If the parties to this agreement separate before that payment is made, then the deal is no longer valid. End quote.

Al-Bahuti said in Kashshaf al-Qina` (8/283): If a person makes a deal regarding something that he owes to someone else, agreeing to give him something else instead, this is a transaction like buying and selling, such as if he acknowledges that he is keeping an item for him or some debt that he owes him, then he gives him something different that is valid to give instead.

This may be divided into three categories: if it is currency for currency, then it is subject to its own ruling, because it is selling one of the two currencies (gold and silver) for the other, so it is stipulated that the exchange be done immediately. End quote.

Based on that, it is not permissible for your sister to take the gold in return for giving money to the other heirs that is to be paid later on; rather the money must be paid immediately after reaching the agreement.

And Allah knows best.