Query to update one column of a table based on a column of a different table
This should solve the first requirement:
UPDATE CTI.Trns_Measure_Two -- Updating Customer_info.Trns_Measure_Two
SET CTI.Trns_Measure_Two = CTI2.Trns_Measure_Two -- Set it to the correct value (the only non-zero value for that Customer_num)
FROM Customer_Transaction_Info AS CTI
INNER JOIN Customer_info AS CI -- Inner joining Customer_info to ensure we only update for the correct Customer and Branch
    ON CTI.Customer_num = CI.Customer_num
    AND CTI.Branch_Code = CI.Customer_Branch
INNER JOIN Customer_Transaction_Info AS CTI2 -- Need to re-join to Customer_Transaction_Info on Customer_num and Trns_Measure_Two &lt;&gt; 0 to get this customer's non-zero correct value
    ON CTI.Customer_num = CTI2.Customer_num
    AND CTI2.Trns_Measure_Two &lt;&gt; 0

This should update the incorrect branches for your second requirement:
UPDATE CTI.Trns_Measure_Two -- Updating Customer_info.Trns_Measure_Two
SET CTI.Trns_Measure_Two = 0 -- Setting incorrect values to 0
FROM Customer_Transaction_Info AS CTI
LEFT JOIN Customer_info AS CI -- Left joining to Customer_info so we can see where there's no match by Customer_num and Customer_Branch
    ON CTI.Customer_num = CI.Customer_num
    AND CTI.Branch_Code = CI.Customer_Branch
WHERE CI.Customer_num IS NULL -- This filters Customer_Transaction_Info to only the bad records (where there's no match to Customer_info)

Please see the comments for information on how these two update statements work.