If it gets on a shared server, you can pull from different sources using different connection strings (using your database or his database, etc.). Here's a sample of connecting to 2 different database using 2 different connection strings in the Config
file.
<connectionStrings>
<add name="Conn1" connectionString="Data Source=YourDataSource;Integrated Security=True"
providerName="System.Data.SqlClient" />
<add name="Conn2" connectionString="Data Source=YourDataSource;uid=YourUserID;pwd=YourPassword;" providerName="System.Data.OracleClient" />
</connectionStrings>
Copying a SQL Server Database will be helpful also, because if a database is on his local machine and neither of you are connected via LAN or some intranet, you can't access it. It needs to be copied or put on a shared server/location where both of you can access it. Otherwise, see the link on how to copy the database.
Copying data from one database to another. This link should also help accomplish the meat of your question.
However, if you solely want "B" to be able to access it, and you don't care about the access, then just deploy your executable and change the connection string in his config file.
Also, see Vladimir's post regarding 'Backup'.