SQLite update: correlated sub-query fills rows in target column with same values

I am trying to update a column of a table with values of another table's column, depending on the values of the updated column in SQlite. Here is an example:

Table 1
A
1
2
3
1
3
4

Table 2
A   B
1   x
2   x
3   y
4   y

Result Table 1 after query:
A
x
x
y
x
y
y

From related questions, I tried the following queries:

update Table1 set A=(select B from Table2 where(A=Table2.A))

This fills col A of Table 1 with all x.

Also, another version I found here did not work, as it threw the error "no such columns: table2.B":

update Table1 set A=Table2.B where(A=Table2.A)

Any help is highly appreciated!