All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Zakaat is connected to the passing of a lunar year and it has nothing to do with a specific month; neither Ramadan nor any other month.
If the wealth on which one is obliged to pay Zakaat reaches the Nisaab (i.e. the minimum amount liable for Zakaat) and a whole lunar year elapses on it, then Zakaat becomes due on it.
The jurists said that it is not permissible to delay the payment of Zakaat except in certain cases and in accordance to certain rules.
Ibn Qudaamah said: "Chapter: If he delays it [i.e. Zakaat] so that he can pay it to someone who is more deserving of it, like a relative or a person in a dire need, and it is a short period, then it is acceptable (to delay it). However, if it is delayed for a long period, then this is not permissible." [End of quote]
It is permissible to pay Zakaat to relatives if they are not parents (and grandparents) or children (and grandchildren). So it is permissible to pay Zakaat to relatives who are eligible for it, like maternal and paternal uncles and maternal and paternal aunts. Relatives are more deserving of it than others because it (giving them Zakaat) includes charity and keeping ties with kinship.
Salmaan ibn ‘Aamer narrated that the Prophet said: "Giving charity to the poor is (considered only as) charity, while giving charity it to the relatives is considered as charity and keeping ties with kinship." [At-Tirmithi]
As for the grandfather, he is among the ancestors [i.e. the origin from whom one is descended], so it is not permissible to pay Zakaat to him. The rule set by the scholars in this is: "Every person whom one is obliged to spend on, it is not permissible for one to pay the Zakaat of his money to him/her.”
Some scholars excluded two cases from this:
Firstly, if the ancestor (a parent or a grandparent) or descendant (a child or a grandchild) is indebted; in this case, it is permissible to pay Zakaat to him. This is because the ancestor is not obliged to pay his descendant’s debt, and the descendant is not obliged to pay his ancestor’s debt.
Secondly, if the money of the person who pays Zakaat is not sufficient to spend on the ancestor or descendant; in this case one is not obliged to spend on him, and so he may give Zakaat to them.
Allah knows best.