North bid 1 and East overcalled 1. When this was passed by South and West, North reopened with 1NT.

What is South's best bid now?

South's bid depends on what he thinks North has. Which range do you expect North to have?

a) 12-15 HCP
b) 16-18 HCP
c) 19-20 HCP

North should have the big one. With 12-15, he would not bid 1NT. It is too dangerous facing a hand that couldn't bid over 1. North should not have the 16-18 range either because he did not open 1NT.

What is left is 19-20, a hand that North had intended to jump rebid 2NT if South had responded at the one level.

Expecting a good hand from North, South should go to 3NT. Lesser bids like Pass, 2, or even 2NT are inferior and do not show the full value of the South hand.