Say you're Belle Lee and you have a bunch of high level commanders from all over the Inner Sphere (including Clanners) and you misjump to another universe where news of the Amaris Coup just broke out and you're relatively close to Kerensky.
He and his staff believe your story, but what advice do you give them? Are there technical details you think could help end the war sooner?
That's a really tough question. I know some excellent ideas have been already suggested (except 1...*slaps pheonixstorm upside the head, then throws him in the brig*...traitorous Amaris supporter... -- just kidding).
The question is probably going to be what kind of information is going to be most helpful to him. Since Kerensky has just been informed of the coup, that makes it too late to do anything to help the Loyalist units that were stuck on Terra or most of the other original Hegemony worlds. So the question does become what kind of information he could use, & how to implement it.
First off, I'm not sure how much technical knowledge would actually help him, or would even be available to give him. Sure, you might have a few examples of Clan tech on board your vessel...but unless this is some high-level meeting between Clan Diamond Shark/Sea Fox & potential Clanner/IS buyers, the chances of having the hard technical data needed for manufacturing the advanced Clan tech is going to be lacking. It's also going to take a long time to try to reverse-engineer the Clan-level technology. I don't have my books handy, but IIRC there's a note in the newer House Davion manual about how Davion engineers had reached the level of technical knowledge to be able to build Clan-level armor & equipment...but were holding off on trying to work on mass-production because it would have resulted in widespread economic disruption (no details given, but I imagine we're talking extended construction downtime for retooling, massive layoffs, massive upticks in unemployment, massive drop in tax revenue collection combined with massive increases in Dole/social program payouts seriously hampering the government's ability to meet its financial obligations, etc.). I could
maybe see being able to adapt some of the Inner Sphere technology that hadn't been developed yet -- ER Medium/Small Lasers would probably be easy given the availability of ER Large Lasers, for example. And I'm sure Kerensky's forces would have loved to have access to C3 technology, or (depending on when your leaders came from) items like Plasma Cannons, MRM launchers & MMLs, etc. But again, you're talking about needing time for retooling & disseminating the technology to your forces, when the biggest problem facing the SLDF during the coup wasn't losing their technology edge (since the Amaris units now had full access to Royal-level manufacturing & technology) but rather actually getting their forces in-system & on-planet to take out the Republic's forces.
Probably there were 2 key items of intelligence that would greatly help out Kerensky:
1. That the Amaris forces had taken control of the SDS units. It's one thing to suspect that your enemy has control of the system defenses;
knowing that they have them, combined with knowing the capabilities of those units & their deployments, would give you at least some advance warning, if not a potential tactical advantage. For example, they might have decided to go with tactics similar to those used by Admiral Lawrence to liberate New Dallas in 2773 (i.e. false-flagging captured Republic WarShips to seize control of the SDS command stations at the main jump points to allow more SLDF forces to enter the system).
2. Having more information about Republic deployments. Having nearly exact knowledge of your enemy's unit deployments -- specific units, unit compositions, manpower levels, etc. -- makes it a whole lot easier to determine how many forces need to be sent into a particular fight.
3. IMHO, probably the most important: perhaps being able to change your overall strategic plan. For example, with more knowledge of how Republic operations had gone, it might have made more sense for Kerensky to focus on liberating Hegemony worlds first instead of hitting the Rim Worlds Republic. Liberating worlds like New Dallas or Carver V, for example, would have provided some nice morale boosts for the SLDF, as well as demoralizing the Republic. If nothing else, I would considered the possibility of focusing on prime worlds -- major supply bases, manufacturing facilities, etc. -- as taking those planets not only is a blow to the Republic from destroying their units, but denies them the material benefits & gives the SLDF much-needed manufacturing & supply capabilities.