Is it permissible for one who is observing a voluntary fast to break his fast during the day, and will reward be recorded for both the one who breaks his fast and the one who causes him to break his fast?

The question is unclear, and the answer pertains to someone who broke a voluntary fast. We are not aware of any scholar who states that someone who breaks a voluntary fast is rewarded absolutely. Scholars have differed on the permissibility of breaking a voluntary fast: the Hanafis and Malikis held it impermissible, while the Shafi'is and Hanbalis considered it permissible with slight disapproval (karahah).

However, if a fasting person breaks their fast for a strong reason, such as being invited to a banquet while fasting, it is recommended for them to break their fast. Ibn Qudamah said: "If it is a voluntary fast, it is recommended for him to eat; because he has the option to break the fast, and if eating involves responding to his Muslim brother and bringing joy to his heart, then it is more preferable."

As for someone who offers food to a fasting person before sunset, they do not receive the reward for feeding a fasting person, because the intended meaning of "feeding a fasting person" for which reward is promised is feeding them at the time their fast ends (at Maghrib). The meaning of "whoever feeds a fasting person" is whoever gives them food at their breaking of the fast.