Is it permissible to present my brother with a sheep for the 'aqiqa [sacrifice made for a newborn] of his newborn since he cannot afford it himself?

If the case is as mentioned in the question, there is no objection provided the sheep is free of any defects, is slaughtered on the seventh day of the child's birth and the child's family as well as both the rich and poor eat from its meat as a sign of gratitude to Allah for being blessed with a child.

The above answers the question and Allah Almighty knows best.