If you have multiple rows in TableA with the same 'Short Date of exam', you may not get the result you want.
If there is only one row for each 'Short Date of exam' in TableA, you may use the script given below to load TableB
SQL SELECT *
FROM `S:\Imaging - Data Repository\Look up tables\M_Calendar\Calendar LUT.accdb`.`M_Calendar`;
LOAD 'Short Date of exam' as DateActual Resident TableA;
Left Join (TableB) LOAD * Resident TempTable;