Reconcile users with logins using 'sp_change_users_login' Sql Server 2008 (and 2005):

I have a Sql Server instance, let's say, InstA, in a Domain (called AD). In that I have a domain Windows Authentication Login, called AD\Log1 that has an associated user, User1 in a database called DB1. 

So, now I backup this database and restore on a new instance (Inst2) that is not part of any domain. It has an existing login (LocalMachine\Log2) that I need to have mapped to the existing User1 in the newly restored database DB1.

With sp_change_users_login, I get the following error:

EXEC sp_change_users_login 'Update_One', 'User1', 'LocalMachine\Log2' 

Msg 15291, Level 16, State 1, Procedure sp_change_users_login, Line 114
Terminating this procedure. The User name 'User1' is absent or invalid.

If I use ALTER USER User1 WITH LOGIN = 'LocalMachine\Log2', it renames the user User1 to LocalMachine\Log2 and maps it to LocalMachine\Log2 login. It works, but I do not want it to rename.

I would prefer to map this existing database user User1 in the database DB1 to an existing login in the new instance inst2 without changing the user name or creating a new login (AutoFix). Just update the SID and map it (without other changes).

Is it possible?

What I gathered so far is, for my situation, sp_change_users_login does not work because LocalMachine\Log1 is a Windows Account (not a Sql Login). but if both were Sql Logins, sp_change_users_login with work perfectly.

Thanks,
When you run sp_change_users_login, it automatically renames users as explained in Books Online:


  The name of the user will be automatically renamed to the login name
  if the following conditions are true. The user is a Windows user. The
  name is a Windows name (contains a backslash). No new name was
  specified. The current name differs from the login name.


To keep life easy, I'd keep the same usernames on both servers and then you should be fine with sp_change_users_login.