If the matter is as you describe, what you want your grandfather to do, giving up his right to inheritance in return for something is called a deal (sulh) by the scholars. In the form asked about here it is a deal agreeing to give up something unknown, because the grandfather does not know the amount of his share of the inheritance. Some of the scholars – such as al-Shaafa’i – regarded a deal to give up something unknown as not permissible, just as it is not permissible to sell something unknown.
Imam al-Shaafa’i (may Allaah have mercy on him) said in al-Umm (3/226): Among the haraam things that happen in deals, as I think, is when the deal is based on giving up something unknown, such as if it were a sale or transaction it would be haraam. If a man dies and some of his heirs make a deal with others and the deal is made with both parties being aware of their rights, or they confirm that they are aware of their rights, and the exchange is done between the two parties before they separate, then the deal is valid. But if it happens when they do not know the amount of their due shares or the amount on which they are basing their deal, then the deal is not permissible, just as it is not permissible to sell something unknown. End quote.
According to Imam Ahmad (may Allaah have mercy on him), a deal may be made concerning something unknown if it is not possible to know it, but if it is possible to know it – as in your question – then a deal is not permissible.
Ibn Qudaamah (may Allaah have mercy on him) said: A deal concerning something unknown may be valid if there is no way of knowing it. But with regard to that which it is possible to know, such as an estate that is present or is known to the one who is in charge of it but its owner is unaware of it, then a deal cannot be done when there is ignorance.
Ahmad said: If a deal is made with a woman with regard to her share of the estate which is one-eighth, it is not valid. He quoted as evidence the words of Shurayh: Any woman who makes a deal with regard to her one-eighth of the estate when she does not know what her husband left, is undoubtedly a very suspicious deal, meaning there is some suspicion that the other heirs want to take her wealth and deceive her.
He said: If some people inherit some wealth and property, and they say to some of them: We will exclude you from the inheritance in return for a thousand dirhams, I regard that as makrooh . Nothing should be bought from her without her knowledge, as she may think that it is a little when he knows that it is a lot. It should not be bought until she knows what it is. Rather a man usually tries to make a deal with another man concerning something that he does not know. But if he knows what it is, why should he make a deal concerning it?! The only reason is that he wants to cheat the other party. End quote from al-Mughni (7/23).
Based on this, it is not permissible for you to ask your grandfather to give up his share in return for money that you will give him, because this may lead to you being accused of wanting to consume your grandfather’s share of the inheritance and deprive him of it, so that it will not go to his heirs after he is gone.
If you really want to dispense with the proceedings that may take a long time, you should work out the inheritance and calculate your grandfather’s share; in that case you will avoid the thing that you fear.
If your grandfather is healthy and of sound mind, and his mind is not affected by his advanced age, there is no sin on you if he gives up all or some of his share, so long as that is with his consent and without you asking him for it, because if you ask him for that he may agree out of shyness.
You must strive to be just and not takes away people’s dues. Allaah Himself has allocated the shares of inheritance, and He says concerning them (interpretation of the meaning):
“(these fixed shares) are ordained by Allaah. And Allaah is Ever All‑Knower, All‑Wise”
So it is not permissible for you to use tricks to take away the rights of others.
We ask Allaah to guide you to make your earning halaal and help you to avoid haraam.
And Allaah knows best.