Lighting Candles in the Synagogue

In a synagogue where the Ark is on the eastern side and it is not possible to place the menorah on a table, but only on a fixed shelf on the wall or a window sill, what is the order of lighting?

In places where it is not possible to place it on a table near the southern wall as mentioned above, and it is placed on a shelf on the wall or in the synagogue window, according to the Shulchan Aruch, one should begin on the first day with the right candle. [That is, the western candle], farthest from the Ark. There is a disadvantage in this as it is not the candle closest to the Ark. On the other days, one lights from left to right [from east to west from the new candle]. According to the Vilna Gaon, one begins with the left candle closest to the Ark, and on the other days, one begins with the left candle closest to the Ark and moves from left to right. [In this manner, the old candle is lit first].

Mishna Berura (Siman 671, Seif Katan 42-43; Shaar HaTziyon Siman 676, Seif Katan 21). According to the Chatam Sofer (Orach Chaim Siman 686; cited in Mishna Berura Siman 671, Seif Katan 43), one should begin lighting from the candle closest to the Ark, as in the Temple, the western candle was closest to the Ark of the Covenant. Therefore, ideally, the candles should be arranged so that the right candle is closest to the Ark, but if this is not possible, this advantage is lost. Azmera Leshimcha (Issue 119).