Answer
(Fatwa: 844/651=L/1430)
If he is doing a lawful job in bank, likewise invests in shares in compliance with Shariah, his income is lawful and he can gift anyone out of the amount. But, if his work in bank involves anyhow helping in interest or he invests in shares without observing the Shariah rules, the income will not be lawful. But, if your uncle is poor, you can give him the amount and he can perform hajj with the amount.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband