Is it permissible to distribute the estate of the deceased, which consists of cash, shares, and real estate, after settling his debts, by dividing each type of asset separately into thirds: one-third for the bequest and two-thirds for the heirs, without the need to disburse the entire one-third for the bequest all at once, especially if part of the estate (such as land) currently has no buyer and there is not enough liquidity to purchase one-third of it to fulfill the bequest, given that some of the heirs are in need of money?

Initiating the execution of a will after the testator's death is a religiously mandated act, oscillating between obligation and recommendation. If the will is obligatory, then its prompt enforcement is incumbent. If it is a voluntary act, then it is sunnah (definition) (recommended).

Based on this, if your father voluntarily willed one-third of his wealth, it is recommended for you to promptly execute his will, but it is not obligatory, especially if it is difficult to immediately disburse the entire one-third. There is no blame upon the heirs for dividing the inheritance and delaying the sale of the real estate until its sale becomes feasible, so that the remainder of the will can be disbursed from its proceeds. It is also permissible to disburse one-third of the value of the real estate instead of the real estate itself.