I agree with Robert, avoid re mapping unless necessary. Create the login with the correct SID, this script is also useful for generating CREATE LOGIN ... statements from a source server. The roles should be pretty easy for you to figure out 😉
SELECT'CREATE LOGIN ' + name + ' WITH PASSWORD = ' +
sys.fn_varbintohexstr(password_hash) +
' HASHED, SID = ' + sys.fn_varbintohexstr(sid) +
', DEFAULT_DATABASE = ' + QUOTENAME(default_database_name) +
', DEFAULT_LANGUAGE = ' + default_language_name +
', CHECK_EXPIRATION = ' +
CASE
WHEN is_expiration_checked = 0 THEN 'off'
ELSE 'on'
END +
', CHECK_POLICY = ' +
CASE
WHEN is_policy_checked = 0 THEN 'off'
ELSE 'on'
END
FROM master.sys.sql_logins
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"Ya can't make an omelette without breaking just a few eggs" 😉