If the deceased has no son, does the brother take the place of the son and fall under the Hadith?

A believer benefits from the supplication of other believers. This is evidenced by Allah's praise for believers who supplicate for their brethren, as stated in His Almighty قول: (And those who came after them say, "Our Lord, forgive us and our brethren who preceded us in faith") [Al-Hashr: 10]. The benefit of restricting the supplication to the child in the Hadith is to encourage the child to supplicate for their parent, due to the right the parent has over them.