The script below will append the text 'Created By: {firstName lastName}', 'Created on behalf of: {firstName lastName}', and 'Updated by: {firstName lastName}' to the end of the note description in cases where the user's Email address was changed on the __M_Users table as a result of User Mapping. 

In cases where the firm's domain has changed, every user's email address will have changed.  In which case the script below will add that information to all notes, which would be redundant for some records.  Therefore, you might want to adjust the WHERE clause.

--Append Created By/Updated By/Created On Behalf Of to Notes
UPDATE
    __M_Common_Notes
SET
    Final_Description = CONCAT(Final_Description, CHAR(10), CHAR(10), 'Created By: ', u.Final_FirstName, ' ', u.Final_LastName)
FROM
    __M_Common_Notes n,
    __M_Users u
WHERE 1=1 
    AND u.Original_Email != u.Final_Email 
    AND u.Id = n.Final_Created_By_Id

UPDATE
    __M_Common_Notes
SET
    Final_Description = CONCAT(Final_Description, CHAR(10), CHAR(10), 'Created on behalf of: ', u.Final_FirstName, ' ', u.Final_LastName)
FROM
    __M_Common_Notes n,
    __M_Users u
WHERE 1=1 
    AND u.Original_Email != u.Final_Email 
    AND u.Id = n.Final_Created_OnBehalfOf_Id

UPDATE
    __M_Common_Notes
SET
    Final_Description = CONCAT(Final_Description, CHAR(10), CHAR(10), 'Updated by: ', u.Final_FirstName, ' ', u.Final_LastName)
FROM
    __M_Common_Notes n,
    __M_Users u
WHERE 1=1 
    AND u.Original_Email != u.Final_Email 
    AND u.Id = n.Final_Updated_By_Id