Yes, it is obligatory for him, as well as for anyone who is required to fast at the beginning of the day; due to the existence of the reason for obligation and eligibility, then it becomes impossible for him to continue: like someone who deliberately breaks his fast during the day of Ramadan, or someone who wakes up on a day of doubt having broken his fast, then it becomes clear that it is a day of Ramadan. It is obligatory for them to refrain for the rest of the day, resembling those who are fasting. Refer to: Al-Mabsut 1: 116, 3: 71, and Badai' al-Sanai' 2: 103; as reported by Salama bin Al-Akwa' (may Allah be pleased with him), who said: 'The Prophet (peace be upon him) commanded a man from Aslam to announce to the people that whoever has eaten should fast the rest of his day, and whoever has not eaten should fast, for today is the day of Ashura,' in Sahih al-Bukhari 2: 705, and Sahih Ibn Hibban 8: 385, and Al-Mustadrak 3: 608. Ashura was obligatory to fast before the obligation of Ramadan. And because the time of Ramadan is a noble time, it is necessary to honor this time as much as possible. If one is unable to honor it by actually fasting, he must honor it by resembling those who are fasting; fulfilling its right as much as possible if he is eligible to resemble them, and to avoid exposing himself to suspicion. Refer to: Badai' al-Sanai' 2: 103.