All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If they are relatives, living together and one of them sponsors them – even if as a donation – then it is permissible for them to share in one Udhhiyah even if it is a sheep.
If one of the three conditions; namely: kinship, living together and sponsoring is not met, then sharing is impermissible.
Therefore, if the owner of this Udhhiyah from among the brothers is the one who sponsors them, then it is permissible for him to let them share his Udhhiyah and it avails for all of them.
Each one of them will attain the reward of an Udhhiyah, Allaah Almighty willing. The owner of the Udhhiyah will attain the greatest reward because he paid while they did not pay.
Allaah Knows best.