Say, a man has a good credit record but his wife has a bad record. The
man applies an additional credit card for his wife using his account
and pays balance in time. And when he applies it he needs to provide
his wife's SSN. After a certain period, will the wife's credit score
be improved?

If the wife has a credit card, which is in her name, and it is paid
off in timely fashion, over time it will improve her credit score.

No.  The person named on an additional card on an account is not
legally responsible for the account, so it will not help her credit
score.  Only the account-holder's credit score can be affected by the
existence and use of the credit card.