Traveller returned home in Ramadhaan during the day and wants to have sexual intercourse with wife

A man returned home from a journey and had not been fasting [due to his travels, so he] decided [now he was at home] to fast [the rest of the remaining day]. He then found his wife taking a bath [since she had] completed her menses; Is it permissible for him to have sexual intercourse with her in this case or should they both assume the fast for the [remainder of the] day?