Is it permissible for a brother to offer the sacrifice with us using the same sacrificial animal we bought, or must he buy a special sacrificial animal for himself?

If a brother lives with his family and shares expenses with them, one sheep is sufficient for them as an Udhiyah. It is also permissible for each of them to offer a sacrifice on their own behalf. However, if their residences and expenses differ, it is not permissible for them to share one sheep.