A person who forgot to recite Arbit one night, or was unable to recite Arbit due to circumstances beyond his control, can make up the missed prayer by reciting an extra Amida the next morning, at Shaharit. So long as the individual did not intentionally neglect to recite Arbit, he is able to make up the missed prayer by adding an extra Amida the next morning.
Until what point in the day can one make up a missed Arbit prayer?
The general Halacha regarding "Tashlumin" (making up a missed prayer) allows one to make up a missed prayer only during the time-frame of the subsequent prayer. Thus, one can make up a missed Arbit prayer only during the time during which he can recite Shaharit. However, when it comes to Shaharit, Halacha establishes two different time-frames. The Gemara in Masechet Berachot writes that one should recite the Shaharit prayer until the end of the fourth hour of the day, in accordance with the view of Rabbi Yehuda. If, however, a person did not pray Shaharit by this time, then he should still pray Shaharit, as long as Hasot (midday as defined by Halacha) has not passed. Although he will not be rewarded for praying at the proper time, he will receive reward for reciting a valid prayer nonetheless. With regard to Shaharit, then, there are two "deadlines" for reciting the prayer: preferably, one should recite it by the fourth hour, but if not, he can recite the prayer until midday.
The question thus arises, if a person did not recite Arbit, and the next day he recites Shaharit after the fourth hour, does he add an extra Amida to make up for the missed Arbit? On the one hand, since he can still recite Shaharit, the time for the "Tashlumin" prayer has not passed. On the other hand, one might contend that the makeup prayer must be recited during the optimal time-frame for Shaharit, which ends after the fourth hour of the day.
This issue is subject to a debate among the Halachic authorities. Hacham Ben Sion Abba Shaul (Israel, 1923-1998) held that one cannot make up a missed Arbit prayer after the fourth hour the next morning. In his view, a Shaharit prayer recited past the fourth hour is essentially a makeup prayer for the prayer that one should have recited before the fourth hour. And since one can make up only the previous prayer, one cannot make up a missed Arbit prayer at the time when he makes up his missed Shaharit prayer. Hacham Ovadia Yosef, however, disagreed. He claimed that Halacha assigns to Shaharit two different time-frames – a preferable time-frame, and a less preferable time-frame. Thus, one who recites Shaharit after the fourth hour is not "making up" a missed prayer, but rather praying Shaharit in its less preferable time, and it is therefore not too late to make up the Arbit prayer which one had missed the previous night.
As for the final Halacha, a person in this situation should follow the "compromise" solution suggested by the Mishna Berura (Rav Yisrael Meir Kagan, 1839-1933). Namely, if a person missed Arbit and recites Shaharit after the fourth hour the next morning, he should recite a second Amida prayer and stipulate that it should count as a makeup for Arbit only if Halacha indeed allows making up Arbit at that point. Otherwise, it should count as a voluntary prayer. By making this condition before reciting the second Amida, one satisfies all opinions.
Summary: A person who forgot to recite Arbit makes up the missed prayer by reciting an extra Amida the next morning, at Shaharit. If he recites Shaharit past the fourth hour of the day, he should stipulate before reciting the second Amida that according to the view that one cannot make up a missed Arbit prayer at this time, the Amida should count as a voluntary prayer.
