Is money obtained from a research institution and deposited as a bank endowment, whose interest is spent on the project, lawful or unlawful? And is it permissible to keep the principal amount after the project ends and its full value has been disbursed from the interest?

This money was given to the inquirer for a specific purpose, so he is entrusted with it, like an agent. The inquirer erred in disposing of it without permission. He must return it to the granting entity or inform them of the situation. If they permit him, he may take it, otherwise not, because the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions." Furthermore, depositing money in a usurious bank and taking usurious interest is a reprehensible act from which one must repent. Spending usurious interest on beneficial public projects falls under the categories of spending unlawful money.