Can one of the heirs give up their rights of inheritance to other deserving members?

It should be noted that inheritance becomes irrevocably part of a person’s property, but if a person wants to give it up after that to other heirs, there is nothing wrong with that. It is, however, highly recommended for all eligible heirs to allow the money to come into their possession first before deciding to relinquish it to other deserving heirs.
If the heir renouncing the inheritance share is rich and does not need this money and wants to pass it on to other deserving heirs, then what they did was a gift, charity, and upholding ties of kinship, and Allah will replace them with something better than this money, Insha’Allah.