[SqlServer] How can I modify data in another table with data in one table?

Q: How can I modify the data in another table using the data in one table based on certain conditions?

A: How difficult is this? use SQL UPDATE.

Table 1	Student
Stu_id	Stu_name	Stu_age
1	Aa	20
2	Bb	21
3	Cc	22
4	Dd	23

The other table is as follows:

Table 2	Lag
Lag_id	Lag_name	Lag_another
1	1111	Abcd
3	2222	Efgh

I want to replace the data in student 1 and 3 with 1111 and 2222 in tables 1 and 3 in lag. The modified results are as follows:

Table 1	Student
Stu_id	Stu_name	Stu_age
1	1111	20
2	Bb	21
3	2222	22
4	Dd	23

The execution statement is as follows:

Update student
Set student. stu_name = (Select lag. lag_name from lag where lag. lag_id = student. stu_id)
Where student. stu_id in (Select lag. lag_id from lag)