Is it obligatory to withdraw money deposited in an interest-based riba bank that offers monthly interest and deposit it in an Islamic bank, knowing that the return in Islamic banks might be implicitly fixed?

It is not permissible to invest in usurious banks, but it is permissible in Islamic banks. If a bank predetermines the interest and fixes it regardless of profit or loss, then it does not operate according to Islamic Sharia (definition), even if its name is "Islamic." This falls under usury, and any funds obtained from it must be given as charity for the general welfare of Muslims, such as roads and hospitals, and to the poor and needy.