Back when Star Trek III: The Search for Spock was released a lot of SFB players noticed that everything that happened in space in the movie was already represented in the game. Even the ending. At the end of the movie Kirk tricks the Klingons onto his ship, blows it up, and winds up on the bridge of the enemy ship and in command of it. This had actually been a rule in SFB already. A "Legendary Captain" has a 1% chance of doing this whenever his ship is destroyed and this rule had existed for many years before the release of the movie. The explanation for this within the SFB rules... "Don't ask how he did it, that's why he's a legend."
Although Star Trek/Paramount has used many things from the Star Fleet Universe in the past, this was more likely a matter of SFB being so complete that it already had the situation covered because it was Star Trek: The Next Generation and the later shows that fairly regularly honored SFB for some unknown reason, in ways that only SFB players would notice.
The most famous is probably that Stephen V. Cole is actually the creator of the term "warbird" for Romulan ships.
And, of course, the TNG episode "Peak Performance" that is a tribute to SFB from beginning to end and even features a character, "Cole-Rami", that is an overblown caricature of Steve Cole written and casted by someone who had clearly at least met him. The SFB references never stop in this episode, and the entire plot is an SFB scenario called "Practice, Practice, and Then What?" The only things non-SFB players are likely to notice are Picard saying "...and so ends the Entperise's first Star Fleet Battle simulation" as the ship sails off into the sunset at the end, and the forced dialog about Cole-Rami that might seem odd too you without understanding why. "Cole-Rami" is from a race that is so respected for their strategic abilities that they have never been challenged in combat, to which Worf replies "Then the reputation is meaningless". I have always thought those who weren't in on the "other" story of this episode might think that those lines were forced and out of place. They are references to the fact that Steve Cole famously does not play SFB (which is part of the reason he created the SFB Staff), and to his most well-known quote "The only valid test is combat, the only valid result is victory" (his "standing order" advice to playtesters as to how they should view their own ideas), attributed within the game to SVC's alter-ego within the storyline... Klingon Grand Admiral Ardak Kumerian.
There is a second full episode of ST:TNG taken from the Star Fleet Universe. In the episode entitled "The Wounded", Captain Maxwell and the Phoenix cross the Cardassian border and preemptively attack them because he is convinced that the Cardassians are preparing to invade the Federation. This is one of the original historical scenarios of the Star Fleet Universe "(SH2.0) The Surprise Reversed" that was one of SVC's original scenarios that came with the original game. In the original SFB scenario, Federation Commodore Anthony J. Stocker crosses the Romulan border to do exactly the same thing. Only in Stephen V. Cole's "Clancy-esq" version of Star Trek, nobody would ever think of trying to stop him... because he's doing the right thing. The Star Fleet Universe is a far more militaristic place than the Star Trek that you know.
As an example of one of the more subtle ways they would honor SFB, in the Deep Space 9 episode where they "Forrest Gump" the ST:TOS tribble episode there is a re-creation of the brief scene of the Enterprise and the Klingon Battlecruiser outside of the station. The reason they didn't use the original scene for this when doing the Forrest Gump thing was obvious to many SFB players... these are not the Enterprise and Klingon ships you know from TOS, these are the Star Fleet Universe versions which are subtly but significantly different than the versions from the original show. The ships in the original show were "flat" and plain. The SFB versions evolved from this with subtle things that make them look much better like ridges, hull plating seams, and other slight artistic enhancements that make them instantly recognizable to SFB players as our versions of those ships.
And, finally, the race you know as the "Zindi" of Star Trek: Enterprise are actually The Interstellar Concordium of the Star Fleet Universe... and you probably never knew it. Watch the first 12 minutes of this video where Josh Spencer, the creator of the ISC and by extension the Zindi, introduces you to one of the most popular races of the Star Fleet Universe...
Ctrl+Click or tap to follow the link"
TNG also used a lot of terms from SFB like "emergency deceleration", and seemed to use SFB to choreograph scenes to make sure that what was being said on screen matched the reality of the situation. Many SFB players recognize most of these things.
I don't think anyone, even Steve Cole, knows exactly why ST:TNG and the later shows chose to regularly honor the Star Fleet Universe in hidden ways, but there is no question that they did.
I'll end the whole series of articles with something a lot of people hear about SFB and think is pretty cool that doesn't really fit in any of these articles... "The Cocaine Rule". Huh? Didn't I tell you that you would want to know about that? The Star Fleet Universe is based only on the original series, and actually largely on half-a-dozen or so specific episodes, the most single inspirational episode being "Balance of Terror" (which was on TV in the background when SVC and a friend were playing a naval game called Jutland... and by the end of the episode were instead using Jutland, and the first two pillars of SFB, to fight with a Federation CA and Klingon D7). In the original series there were "Orions", which in SFB are a favorite race... pirates with optional weapon mounts! In addition to their stealth ECM bonus and option mounts, another special ability is to double their engine power (...because Spock says they can in that episode) but doing so destroys an engine box. In SFB this came to be known as "The Cocaine Rule" because... once you start, you can't stop, and it eventually kills you.
And finally, in one last attempt to convey just how "massive", in today's terminology, SFB actually is, I'll leave you with an old saying that most SFB players have heard before... "Star Fleet Battles is not a game, it is a lifestyle choice."