There's no such star as "Archernar," though an IDW comic did give that name to a star system in its Mission's End
comic. The real star, and the one where Heliopolis was located (Alpha Eridani), is named Achernar, and is pronounced to rhyme with either "Laker star" or "hacker bar."
We know that as of the 24th century, Achernar is within Romulan territory; it was briefly the capital of the Imperial Romulan State. So we can assume that the Romulans retained the system after the war. Which makes it a good thing that the Mission's End
writers made that mistake, since it means "Archernar" would have to be a separate star system.
Other than that, I can't say. I know some people feel there are threads that the Romulan War novels didn't address to their satisfaction, but it's not my job to play cleanup or to write The Romulan War Book Two and a Half
. I'm telling the next story, making a new start.