If someone puts me in their will as a bequest [waṣiyyah], can I make a bequest with that wealth to someone else in case I die first?

In the of Allah, the Compassionate, the Merciful.

Summary: No, because you do not own that money yet, and if you die first, that wealth would never have belonged to you at all.

It is allowed, and in some cases, recommended, to leave wealth to a specified person, or cause, after your death. This is known as a bequest [waṣiyyah]. You may not leave a bequest to someone who will already inherit according to Islamic guidelines, such as your children or parents, since that would unfairly increase the shares of specific individuals who are inheriting. Also, the bequest must not be more than 1/3rd of your property, so that the inheritors like children and parents are not deprived of your wealth [estate]. For example, Umar may decide to leave 10% of his wealth after his death to his best friend Ali, since he always helped him throughout his life.
Wealth from inheritance only transfers after the death of a person. For example, in the above scenario, if Umar already wrote the bequest for Ali in his will, that wealth will not belong to Ali until Umar actually dies. If Ali dies prior to Umar, the bequest of Umar is void. So if Ali wanted that wealth to go to his own mother, in case he died first, he cannot write a bequest to that effect, since you cannot transact with wealth that does not belong to you. However, Ali may request that Umar write in his will that if Ali dies first then the wealth will go to his mother. It is Umar’s decision whether to honor that request or not.

[Shaykh] Mustafa Umar
California Islamic University
Fullerton, CA – USA – 2018