SQL Server 2005: Move account from one server to another while maintaining unknown password

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http://serverfault.com – There is a user account that someone set up on one of our database servers long ago, that no-one any longer knows the password for. However some apps have the password (for various reasons we cannot recover the password from the apps). Unfortunately we want to point the apps at a new server and will backup and restore the relevant databases to this new server - is there a way to copy the login from one server to the other keeping the password value as whatever it was before? (HowTos)