What is the ruling on a partner withdrawing from a project after delays in obtaining licenses, and am I obligated to pay what he considers a debt?

Whatever was spent from the partner's capital on procedures, if the second partner entered into the partnership on the basis of considering and compensating for these procedures, then you must return what you were compensated for to your first partner and take nothing from him. If the procedures have no estimable value, then you are not obligated to bear what was lost from your partner's money, as the agent in a Mudarabah (partnership) is not liable except in cases of transgression or negligence. These matters often lead to disputes and are resolved by presenting them to the Sharia courts.