Is it obligatory to pay the value of the household items (qa'imat al-a'yan) mentioned in the marriage contract to my deceased brother's wife before distributing the inheritance? And for this purpose, should the list pertaining to the marital apartment in Egypt, which was not furnished, be considered, or the apartment in Saudi Arabia where they used to live? If the answer is that it is the apartment in Egypt, is it then obligatory to pay her money or to buy the items mentioned in the list?

The list of movables in Egyptian custom is part of the Mahr (dowry) and is a right of the wife that is not forfeited if her father fails to fulfill what was agreed upon. It is obligatory to pay off her debt before dividing the inheritance, whether what was agreed upon was paying half of its value or bringing the items themselves, with the permissibility of paying its value with the wife's consent on the day of payment. As for the apartment in Saudi Arabia, the list has no relation to it. If it was owned by your brother, it is part of his inheritance to be distributed among his heirs. If it was rented, it is to be returned to its owner.