The Rema in OC Simman 242 brings a minhag to eat "pashtidah" shabbos night in memory of the munn. The Beur Halacha is very bothered why one would do such a thing on shabbos, given that the munn specifically didn't fall on shabbos. He brings an explanation he likes from the Tosefes Shabbos citing Toras Chaim:
והוא לפי דשבת בראשית הוא דוגמת שבת שלע"ל שהוא יום שכולו שבת ולכן אנו עושים כמה דברים בשבת זה דוגמתו היינו לאכול בשר ודגים נגד סעודת שור הבר ולויתן ומקדשין על היין נגד היין המשומר בענביו לצדיקים לע"ל...ולכך שפיר יש לעשות בשבת זכר למן ההוא [תוספות שבת]׃
The reason is that shabbos is a sneak peek at the shabbos of Olam Haba, which is a day that is entirely shabbos. Therefore we do many things on our shabbos similar to that of the future Shabbos. Meaning, we eat meat and fish corresponding to the Shor HaBar and the Leviasan and we say kiddush on wine corresponding to the wine that is preserved for the tzaddikim in the future... therefore it is fitting to [eat pashtidah] on shabbos, commemorating that munn
Even though he doesn't explain it, it sounds like he is saying there will be munn in the world to come (although the word זכר seems awkward with this usage). I haven't heard of this concept before and I am wondering if this is something the Toras Chaim developed or is there an earlier source for munn in Olam haba? Not that these things are easy to understand but I'm also wondering what its purpose will be. Will it be eaten? (Chazal say there will be no eating in Olam haba, although what's with the other foods mentioned above I'm not sure).