Is it permissible to give charity on behalf of the deceased as a perpetual charity (Ṣadaqah Jāriyah), and is it permissible to contribute to the construction of a mosque from the profits of a deposit in an Islamic bank?

It is permissible for a living person to perform an ongoing charity (sadaqah jariyah) on behalf of the deceased. The profits from deposits in Islamic banks are lawful earnings, and it is permissible to use them for building mosques or participating in their construction. The doer will be rewarded for seeking the countenance of Allah, for whoever builds a mosque for Allah, Allah will build for him a house in Paradise.