Are the profits from legitimate trade, established with ill-gotten gains that were subsequently returned to their source, considered permissible?

You must seek forgiveness for past unlawful dealings. It is permissible to take profits from unlawful transactions to start a permissible business if the person is poor and has no other money, because this money is not to be abandoned; rather, it should be spent on the poor and needy, including the person and his family according to their needs. Al-Ghazali, Al-Nawawi, and Ibn Taymiyyah stated that it is permissible for a poor person to give charity to himself and his family from unlawful money to the extent of their need, because he is poor like others, and this money should not be destroyed. If the business is profitable, it is not obligatory to give out an amount equivalent to the money you took, but it is better.