Moonlight Syndrome:
The last survivor of the Moon Murders, Yayoi Itsushima, actually shows up in Flower, Sun and Rain under the alias of Yayoi Hanayama.

Unfortunately, Yayoi doesen’t really address any of the events from Moonlight Syndrome. She’s moved on with her life, and she’s merely taking a vacation in the Flower, Sun and Rain hotel.
Ironically, the only survivor from Moonlight Syndrome, was actually aligned with the villain Mithra. That is to say that Yayoi, was indirectly responsible for the death of the rest of the cast.
The Silver Case:
Flower, Sun and Rain takes place in 2001, two years after the beginning of The Silver Case. It initially presents itself as a stand alone experience. The first hint of the game being a sidequel to The Silver Case happens during the Ave Maria chapter, during which the two spouses to be claim to have been raised in the Shelter.
An obvious callback to the Shelter Children Policy from The Silver Case, in which various children were kidnapped and mindbroken to create obedient citizens that could also be activated as killing weapons by their handlers.
Daizaburo Kai and Sundance Shot, respectively the Chairman of the TRO/CCO alliance and the FSO Party leader, while they never appeared directly in The Silver Case, were both named in the original Playing Manual.
Sundance Shot also appeared in the original TSC intro video:
The in-game guidebook also makes explicit reference to Sayaka Baian, the idol who committed suicide in the Kamuidrome chapter in TSC.
After the Claire de Lune chapter, in which Sumio Mondo is shot and seemingly killed by Sundance Shot, two Federal Special Agents come to investigate his death and the Euro Maspro. One of those two agents, Koshimizu Yoshimitsu, is revealed as being the apprentice of Assistant Commissioner Morichika Nakategawa, a member of the Heinous Crime Unit from The Silver Case.

After being returned to life, Sumio Mondo is acquainted to Sundance Ritz, a member of the same clan as Sundance Shot, who reveals to him the truth of the genocide of the Sundance people ordered by Uminosuke Hachisuka.
Uminosuke Hachisuka, under the falsely assumed identity of his son Kaoru, was the mayor of the 24th Ward in TSC and one of the heads behind the Maspro project and the Shelter Children policy.
The purpose of the Sundance genocide was to take over their technology, namely the Silver Eyes, which are cultivated through a specific breed of hyena.
The timeline is unclear on wether The Silver Case (the attempted murder of the TRO/CCO alliance leaders at the hands of Format Kamui, implied to be an ethnic Sundance, in 1979) was ordered in retaliation against the Sundance genocide, or vice versa. I choose to believe the latter, that is to say, that the Sundance genocide happened in retaliation against The Silver Case, specifically because Hachisuka might have been unaware of the connection between the Sundance clan, the FSO party and the Silver Eyes before the attempted assassination, and because the Euro Maspro seems to be a success in harvesting Silver Eyes as opposed to the Kamui and Ayame maspros, implying that it took place at a later time. It is however possible that the Hachisuka clan (backed by the ELBOW group) was the original aggressor, and that they just took longer to reverse engineer Sundance technology.
In short, the clash between the Sundance and Hachisuka clans, resulted in the Hachisuka clan exterminating the Sundance people (save for Ritz and possibly Shot, who might just be a spirit lacking a body however) and reverse engineering their ancient technology, the Silver Eyes, an important plot device from TSC.
After meeting with Ritz, Sumio Mondo is finally able to meet up with Tokio Morishima, one of the main characters of TSC, in a chapter titled “Kill the Past” (Kamui Uehara’s catchphrase in TSC).
The HD re-release of The Silver Case also included an extra chapter, showing Tokio making his way to Lospass island.
The final connections are revealed at the very end of the game: Sumio Mondo is explained as a different persona of Sumio Kodai, a member of the Heinous Crime unit and undercover terrorist in TSC; it’s implied that the Sumio Mondo persona has been implanted into Kodai in order to make him easier to manipulate, or that he might have simply repressed the traumatic memories of being Sumio Kodai.
This creates some measure of confusion because Sumio Mondo, and therefore Kodai, is openly stated to having been a victim of the Euro Maspro Shelter Children Policy. However, the original Shelter Children Policy dates back to 1980, a year in which Sumio would have been living in Mikumo-77.
My explanation for this, is that I believe the Euro Maspro took place after the Kamui and Ayame Maspros, placing it some time in the mid 80s. The Euro Maspro seemingly managed to harvest Silver Eyes, while the Kamui (1980) and Ayame (1984) maspros were considered failures. Moreover, the Euro Maspro apparently makes use of some sort of cloning/replicant technology, where several different stock bodies identical to the original are created from a sample (in this case, the Shelter Children), likely in an effort to replicate Sundance society; Sundance Shot mentions how the Sundance people all shared the same personality and biology.
Keeping that in mind, there is no contradiction in Sumio Kodai taking part in the Mikumo-77 incident and later being abducted as part of the Euro Maspro Shelter Children Policy. In FSR, it is made clear that the Euro Maspro had no sex segregation within its subjects, and that children were abducted all over the world unlike the previous Maspros, which were exclusively located and operated within Japan.
For a final connection, Sumio Mondo’s handler, Peter Bockwinkle, is revealed as Tetsugoro Kusabi wearing a muppet suit, which he promptly removes once it gets too hot.
The 25th Ward:
During the course of the game, RAB agent Osato makes use of a miniaturized version of Catherine, the code breaking machine used by Sumio Mondo in Flower, Sun and Rain.

Sumio Mondo returns in the game as well, though under his original persona of Sumio Kodai, and seems to have retained his abilities as a searcher.
Meru could have been a victim of the Euro Maspro Shelter, though the game does not confirm this outright.
(She mentions being part of the third batch of Shelter Children, which might be referring to the Lospass Shelter, but the details are unclear; she may have been referring to an otherwise unknown batch of kidnappings.)
The system engineer behind the 25th Ward may or may not be Stephan Charbonie from hotel Flower, Sun and Rain; though he is never shown, he does have a similar speech pattern and mentions his inspiration.
Mokutaro Shiroyabu/Shimohira might be part of the Next Maspro mentioned at the very end of Flower, Sun and Rain. His multiple, identical bodies are definetly reminiscent of the cloning/replicant technology seen in Lospass Island’s Shelter at the very least.
The idea that each Shiroyabu was living its own life unaware of the others, helps to retroactively explain the appearence of sixteen Mondos at the end of FSR; It can be inferred that before being summoned to Lospass Island, each Sumio might have been leading an independent life, though this is never actually spelled out within the game.
Killer7:
As I explained in the What is Kill the Past page, Killer7 is set in an alternate timeline, incompatible with that of the other games.
Despite this, I theorise that in earlier stages of development, Killer7 might have been intended as a follow-up to certain storylines in Flower, Sun and Rain. If you want to learn more about it, check out this page:
Killer7 as a follow-up to Flower, Sun and Rain?