This is what I used:
sp_change_users_login 'update_one', 'CRMReplication', 'CRMReplication'
Msg 15291, Level 16, State 1, Procedure sp_change_users_login, Line 114 Terminating this procedure. The User name 'CRMReplication' is absent or invalid.
I'm going to try and find the long sid in AD or in another SQL Server/database. I've worked with SQL for too long to believe it would just make one up.