You can certainly us the same login you had on your original DB install, but you will need to run a script (see below) to correct the orphaned SID of that user. So in short, after your DB transfer, create the same login for your new DB as it is in your web.config and run the following script (2 parts) in query anaylizer to fix the orphaned SID (replace the values in brackets with your own) .

--Detect orphaned users

USE [YOUR_DB];
GO
sp_change_users_login @Action='Report';
GO

--Resolve an orphaned user

USE [YOUR_DB];
GO
sp_change_users_login @Action='update_one', @UserNamePattern='[YOUR_USER]', @LoginName='[YOUR_USER]';
GO

HTH

The SP is installed natively. It is located 'master\programability\stored procedures\system stored procedures'.