Is Zakat obligatory on money from the sale of a house, if a year has passed on it before another house is purchased with it?

If a Muslim owns an amount that reaches the nisab (minimum threshold) and a hawl (full lunar year) passes over it, zakat becomes immediately obligatory on him, and he is not permitted to delay it, whether the money is from the sale of a house or anything else. However, if he buys another house with it before the end of the hawl, then there is no zakat due on him.