You can install a ftp server program, make an account for your brother, let him log in, preferably with a ftp client installed and download whatever files you will allow him access to.
A great freeware ftp server is GuildFtpd http://www.guildftpd.com/
A great freeware ftp client is SmartFtp http://www.smartftp.com/
It's possible to do it in reverse, meaning your brother will install the server and you will log in and upload to the account he will make for you.
Remember that the transfer rate from you to him will be limited by your max upload speed and his download speed regardless who runs the server.