It is customary to eat Matzah in honor of Pesach Sheiyni.
When? Many are accustomed to eat Matzah on Pesach Sheiyni, on the day of the 14th of Iyar. Some are accustomed to eat it towards the afternoon. Others are accustomed to eat Matzah [only or also] on Motzei Pesach Sheiyni, which is the night of the 15th of Iyar. Others eat on the night of the 14th. Those that are most scrupulous eat Matzah all three times.
The Chabad custom: Our custom is to eat Matzah during the day meal of the 14th of Iyar. The Rebbe himself however ate the Matzah many years on the night of the 15th. This custom as also mentioned in talks of the Rebbe. As stated above, the Rebbe states that those that are meticulous eat Matzah three times, once on the night of the 14th, once by the day of the1 4th, and once on Motzei the 14th.
 All Poskim to be listed below
Other opinions: Some do not eating Matzah at all on Pesach Sheiyni. [Maaseh Rav 181; Revivos Efraim 2/129 that so was the custom in Lita; The Chazon Ish did not eat Matzah on Pesach Sheiyni, brought in Nitei Gavriel 57 footnote 15]
 Igros Kodesh 2 p. 352 [however see footnotes below]; Siddur Beis Yaakov; Darkei Chaim Veshalom 631-632 that so was the custom of all the students of the Baal Shem Tov; Shaar Yissachar Pischa Zeira 12; Poskim recorded in Nitei Gavriel 57 footnote 13 and that so is the worldly custom.
The reason: As the sacrifice of the Pesach offering occurred on the 14th. [Darkei Chaim Veshalom ibid]
 Rebbe in Sichas Shemini 1980 28; Nitei Gavriel ibid
 Darkei Chaim Veshalom ibid
 Likkutei Mahrich 44; The Rebbe’s custom of many years as recorded by Rav Groner; In a list of Sichas the Rebbe mentioned the custom to eat Matzah on the night after the 14th. [See Otzer Minhagei Chabad Iyar 44]
The reason: As the meat of the Karban Pesach was only eaten on the night of the 15th.
 Rebbe in Sichas Shemini 1980 28; brought in Otzer Minhagei Chabad 44
 Igros Kodesh 2 p. 352 based on the custom of the Rebbe Rayatz; Hiskashrus 1033
 Rabbi Leibal Groner