Your brother will need to purchase a transfer at that other registrar. Once purchased, they can enter the authorization code you provided to enable that registrar to make the request. When there is a valid request made to the Registry, they will move the domain(s) in your account to a "pending transfer" status. If you see the status in your account reading "pending transfer", or moved to your transfer screen (in the "Domains" drop-down menu in the Domain Manager), you can approve the transfer in the GoDaddy account.
TLH - GoDaddy | Community Moderator Supporting you at x.co/247support