So, if a magus wants to steal the secrets of a Mystery Cult, specifically, initiate the virtues, or integrate their virtues into Hermetic Magic, how would they go about doing this?
In my mind, a magus would to either:
1.) Spy on the Mystery Cult to learn the Mystery Cult Lore and Scripts from Exposure
2.) Steal books on Mystery Cult Lore and the Scripts
3.) Bypass the above and integrate the magic directly into Hermetic Magic by steal Lab texts that use Mystery Cult Virtues or sttudy a magic item as a source for Insight and use Hedge Magic rules. Might require for example, to find one of Verdituis's original rings to begin to steal Verdituis Magic virtues.
Mind reading cult members, blackmailing cultists into revealing secrets, raising the ghosts of dead members of the cult to torture them for secrets (they may have been dead for centuries or minutes, depending), petitioning the patron spirits of cultists (daemons, especially appropriate for Therugic cults), join the cult under a false identity (great for Tytalus) and betray them later.
Beware, though. If you Initiate, your script includes a Vow and you break the Vow, you have essentially taken the Major Story Flaw "Storyguide's Chew Toy" instead
If I just wanted a single Virtue that produced lab texts or items, I'd probably go the Integration route (Hermetic Numerology, for example, is a Virtue where I'm all "Why hasn't this been Integrated yet?"). Cult Lore, sadly, is hard to learn from books unless the Mystery Cult produces summae of its rites for some reason (I imagine most don't because personal instruction); also, not a lot of Mystery Cults have high Lores, as a lot of them rely on harsh Ordeal sequences instead. I would hypothesize that some of the strictly-hierarchical Mystery Cults are strictly hierarchical partly because they don't rely on highly-skilled Mystagogues, but instead build Initiations on prior Ordeals.
One more option (depending on your troupe) would be to get the Initiation Script for a Mystery Virtue (or better yet a Cult Lore summa) and then transform the Virtue through a couple adventures or study seasons in the Magic Realm. Ask your troupe before doing something like that, though (studying inside a Magic Realm boundary is an area that seriously needs clarification).
