Prova detta:
SELECT a.First_Name, b.Dept_Name, alt.Min_Salary AS Min_Salary
FROM table123 a
INNER JOIN table246 b
ON a.Dept_ID = b.Dept_ID
INNER JOIN (
SELECT Dept_ID, MIN(Salary) Min_Salary
FROM table123
GROUP BY Dept_ID
) alt
ON b.Dept_ID = alt.Dept_ID
WHERE a.Salary = alt.Min_Salary;