On February $1,$ Year $4,$ Hall learned that he was bequeathed $500$ shares of common stock under his father's will. Hall's father had paid $$2,500$ for the stock in Year $1.$ Fair market value of the stock on February $1,$ Year $4,$ the date of his father's death, was $$4,000$ and had increased to $$5,500$ six months later. The executor of the estate elected the alternate valuation date for estate tax purposes. Hall sold the stock for $$4,500$ on June $1,$ Year $4,$ the date that the executor distributed the stock to him. How much income should Hall include in his Year $4$ individual income tax return for the inheritance of the $500$ shares of stock, which he received from his father's estate?

A$.$

$$5,500$

B$.$

$$4,000$

C$.$

$$2,500$

D$.$

$$0$