What is the legal status of a bequest to an heir when only some co-heirs provide approval?

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If a testator leaves behind three sons and a slave, which is his sole property, and bequeaths the slave to one son, or gifts it to him during his final illness, the following applies based on the brothers' approval: If both brothers approve, the slave belongs entirely to the designated son. If only one brother approves, the designated son receives two-thirds of the slave (his own share plus half of the approver's share). If both approve half of the slave, he receives half, and the brothers retain the other half. If one approves half of his share and the other rejects entirely, the designated son receives the full slave: his own third share plus one-sixth from the approving brother's share.