All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If you intend by your question that the above-mentioned relative will grant you something from his property which he makes conditional on his death, such as to say, "If I die, you shall have such-and-such of my property", that is a bequest. One has the right to bequeath something of his property, no more than one-third, to anyone who is not his heir. It was narrated in both Saheehs on the authority of Sa‘d ibn Abi Waqqaas that he said, “I said, ‘O Messenger of Allaah! May I will the whole of my property (to be given in charity)?’ He said: ‘No.’ I said, ‘Then may I will half of it?’ He said: ‘No.’ I said, ‘One third?’ He said: ‘Yes, one third, yet even one third is too much. It is better for you to leave your inheritors wealthy than to leave them poor, begging people."
If the bequest is more than the third, or if it is made to anyone of the heirs, it becomes conditional on the approval of the other heirs, in view of the statement of the Prophet, sallallaahu ‘alayhi wa salam: "Allaah has given each (one of the heirs) his right (of inheritance) that is due to him. So, no bequest should be made to an heir." [At-Tirmithi; and Ad-Daaraqutni who added the following in his narration: "…unless the heirs will."
According to Al-Haafith Ibn Hajar in Buloogh Al-Maraam, its chain of narrators is good. However, he said in Al-Fat-h, "Its men (transmitters) are reliable, but it has weakness, for it was said that ‘Ataa’ Al-Khuraasaani, who narrated it from Ibn ‘Abbaas did not hear it directly from him."
Anyway, the majority of scholars acted upon that Hadeeth, and validated the will made to the heir even beyond the third, should the other heirs approve of it.
However, if he has granted it to you as a gift while he was in good health and his legal competence for disposal was effective, and you received it (before his death), then, it is yours, whether or not the heirs willed.
In sum, a gift is that which one gives to another during his lifetime, and in order to be validated, the grantor should give it while being in good health and his legal competence for disposal effective. That is, to be rational, sane and not suffering from a fatal disease. It is also a requisite that the grantee should take possession of it before the grantor dies or becomes bankrupt. If the grantor dies or becomes bankrupt before the grantee takes possession of the gift, it should be returned to the heirs in case of death, and to the creditors in case of bankruptcy.
Allaah Knows best.