update multiple table refrencing new table data

I have a table called ADSCHL which contains the school_code as Primary key and other two table as RGDEGR(common field as SCHOOl_code) and RGENRl(Original_school_code) which are refrencing the ADSCHL.

If a school_code will be updated, both the table RGDEGR (school_code) and RGERNL ( original_schoolcode) has to be updated as well.

I have been provided a new data that I have imported to SQL server using SSIS with table name as TESTCEP which has a column name school_code. I have been assigned a task to update the old school_code value (ADSCHL) with new school_code (TESTCEP) and make sure the changes happen across all 3 tables.

Can someone please help me with this?

I tried using Merge Update function but wasn't able to do it. It errored out.

I tried using this query and wasn't sure if this is gonna help me to update all the tables:

UPDATE dbo.ADSCHL 
    SET dbo.ADSCHL.SCHOOL_CODE = FD.SCHOOL_Code
FROM dbo.ADSCHL AD 
INNER JOIN TESTCEP FD
    ON AD.SCHOOL_NAME = FD.School_Name

via Chebli Mohamed