sql script to export table's column data to another table's column
An update with a simple join will work.

CREATE TABLE Table_A
    (ID varchar(3) not null, Number int not null, Column3 varchar(5), Column4 varchar(5))
;

INSERT INTO Table_A
    (ID, Number, Column3, Column4)
VALUES
    ('ID1', 1, 'AAA', 'BBB'),
    ('ID1', 2, 'CCC', 'DDD'),
    ('ID2', 1, 'EEE', 'FFF'),
    ('ID2', 2, 'GGG', 'HHH')
;



CREATE TABLE Table_B
    (ID varchar(3) not null, Number int not null, Column3 varchar(5), Column4 varchar(5))
;

INSERT INTO Table_B
    (ID, Number, Column3, Column4)
VALUES
    ('ID1', 1, 'AAA_1', 'BBB_1'),
    ('ID1', 2, 'CCC_1', 'DDD_1'),
    ('ID2', 1, 'EEE_1', 'FFF_1'),
    ('ID2', 2, 'GGG_1', 'HHH_1')
;

alter table Table_A 
add constraint pk_ID_NUM_A PRIMARY KEY (ID, Number)
go
alter table Table_B 
add constraint pk_ID_NUM_B PRIMARY KEY (ID, Number)

select * from Table_A
select * from Table_B




Now run the update :

update Table_A
set Table_A.Column3 = Table_B.Column3
from Table_A inner join Table_B
on Table_A.ID = Table_B.ID
and Table_A.Number=Table_B.Number


Below is the expected result that you want :

select * from Table_A
select * from Table_B