Is expiation obligatory for a person and his wife after intercourse during the daytime in Ramadan while traveling, bearing in mind that they arrived at their destination on Monday and had intercourse after noon on the same day, and the questioner will depart alone on Thursday?

If a husband and wife are traveling a distance that permits shortening prayers (masafat qasr), and they arrive at their destination, then the husband intentionally has intercourse with his wife, there is no sin upon them for that, nor is there expiation (kaffarah). Rather, they only need to make up the fast (qada'), because a traveler is not blameworthy for breaking his fast, even if it is through intercourse.