What is the appropriate response to someone who says: "Thank you," and is it permissible to say: "Thanks be to Allah (Ash-shukru lillah)"?

Thanking the doer of good is legislated, and it is done by supplicating for him, such as saying: "May Allah reward you with good." And he who does not thank the people does not thank Allah. It is recommended to repay the doer of good if possible, otherwise, supplicate for him. It is legislated to combine supplication and praise.