If my memory serves correctly we are on the trail of the lady Adelmo, following her path to discover the Syphar N Kalar an ancient Sith... thing, whose nature we don't quite understand.
We met with Alik Saar, who revealed that Kuylen from years past worked with Adelmo at some point, along with a wealthy investor Gene Lennah, in search of Sith artifacts (Can't recall if it was specifically the Sphar N Kalar or something else.) After some kind of falling out Kuylen left to pursue Avalar. Adelmo and Lennah then attempted to locate the Scrolls of Bandimo, a record of Sith victories that may have information on the Syphar N Kalar.
Through some more talking with Saar we discovered that Darth Kazan, an agent of Darth Malphas, likely possessed it during the Malphan wars. The planet we're leaving now was once in control of the Sith and besieged by the Republic. Not wanting the scrolls to fall into the Republic's hands Kazan had them split in two and smuggled off world. We infiltrated his old base and extracted the base logs to hopefully locate where the scrolls were sent.
Now we believe we've narrowed down where this half of the scroll could be to a hand full of, we're going to see Saar to see if he can narrow it down further for us.
I think that sums it all up, though I've lost/forgotten where the other half of the scroll is. In possession of Adelmo I think?
Kuylen/Adelmo/Lennah worked together on the trail of Sith stuff in general- but despite the work he did looking for Avalar and the Mausoleum of Demnos, Kuylen drew the line at the SnK which he did not believe had any functional existence. Adelmo and Lennah kept working on it together, Kuylen and Saar went on to form the eventual Dark Side group that this game has portrayed.
Your understanding is indeed that Adelmo has half of the scrolls, though like most things in this story you are wary of being certain.
Because if we follow Adelmo's path, we can learn just how close she feels she is to achieving her goals and what she learned on that journey to obtain the Scrolls.
They got the half of the Scrolls in the Antigone system, and we're tracking where they may have found the other half currently. Saar claims to not have known where the other half would be and sent Lennah and Adelmo to Alambritis in pursuit of it.