Let's say I'm a member of the Cult of the Earth and get my hands on an initiation script from the Order of the Green Cockerel that lets the Mystagogue initiate Hermetic Alchemy. Is there a way to integrate the script into my cult so I can benefit from Cult of the Earth Lore? Is it just a modification requiring the change of a component (EF 9)? Or do I have to experiment?
Experiment. A lot.
Not sure if i can answer this , but what the hey.
The Mysteries , page 17
Modifying the Initiation Script: Stress Die + Intelligence + (Mystery Cult) Lore vs. Ease Factor
You want to add a new component to the Script for your own Mystery , then Ease Factor is 09.
I think the key is needing to have understanding of the foreign Mystery.
From page 13:
Experimental Scripts (page 18)
If you have no Initiation Script or an inadequate one ,
then you may experiment to discover a new Script.
My feeling is , that unless you can decipher the unknown Script ,
you have to experiment as if you had no Script.
The general intent is that Mysteries , are , mysteries.
It should not be easy , if you steal/find/research Cult Lore(s)
to integrate them into one Arch-Mystery.
Maybe you need to do research on a level similar to that in Ancient Magic to do this.
It would not be as difficult , but you need to spend time doing it and earn breakthrough points.
Consider it this way...
You're a devout member of the Kool-aid Aliens Web Designer Cult, and you're trying to find a ritual that will improve your abilities before you perform the ritual to join the Mothership. You find a ritual of the ancient hellenistic Eleusinian Mysteries cult which supposedly helps with Visions. Will it work? How does it incorporate into your cult, are the beliefs compatible? Do they touch upon similar truths? Can they be incorporated?
Yeah.
I'm going to go with experimentation, at a minimum, presuming your SG is cool with trying to incorporate disparate cults into one cult like that...then you're starting to tromp into deep Crowley territory.
-Ben.
Single best Mystery cult question reply ever. Sums up most questions anyone might have! 
Or the other way around: You're trying to recreate the ancient Eleusinian Mysteries, and you got your hand on some instruction code from the Kool-Aid Aliens Web Designer Cult. The key parts are written in Klingon using the Elven alphabet. It is full of pop culture references and mystical comments about linked objects and loop increments which you don't understand at all, not to mention a few creative spelling mistakes. There are a couple of intentional mistakes in the script too, which would be obvious to a Web Designer, such as missing end comments, and one crucial step, be sure to save before you run the program, has been omitted entirely... But it promises to initiate you into the Mystery of Visual Basic, which should be helpful to your quest of mastering basic visions...
It's going to take massive amounts of research just to translate the thing into a language you speak and run down the obscure references, not to mention acquiring the strange components you'll need - and your instructions strangely neglect to mention things like operating system or compilers, so you'll have to deduce them on your own. Once you have all the components, you'll follow the steps to the letter... and will still trash your computer. If you persevere, after years of study and experimentation you might finally get it right... and find that it has nothing to do with visions after all.
I remember that the Neo-Mercurians do this stuff: search and adapt Mysteries from different Traditions and Cults for themselves, and probably the Disciples of the worm too.
if writing them in Visual Basic is the price for vision, it's a rather steep one I think! 
The Children of Hermes certainly do! 
Yes, you can do this. I think you need to get little lore form the Cult you are stealing from, but certainly in the real world in the 18th century many initiatory societies stole and adapted each others rites, and it was our intention that you could do this. I'm pretty sure Neil included rules for it. I'll go look.
cj x
But in TMRE that's the idea behind Children of Hermes: Hermes knows how to adapt scripts from others. That is their mysterious lore. But that doesn't imply other mystery cults all can.
Chris
Good point. I wrote the Children of Hermes (in fact all the example Cults), and was one of the two authors on TMRE, but it's a good while ago. Let me check what we wrote 
I think you have to actually learn the Cult Lore of the Cult whose script you are trying to adapt, if my memories of the Disciples of the Worm are correct.
cj x