There are companies that specialize in stabilizing woods and other materials, but it is possible to do yourself.
Basically, you purchase a cheap vacuum pump from harbor freight (the kind used to evacuate refrigeration lines), and a plastic bell jar (heck, you could even use some ABS pipe with endcaps, but it's nice to be able to see).
If you mix up some epoxy resin, preferably some formulated for working with composite fibers, you can use it to stabilize the material.
All you need to do is make sure it's very dry by placing it in a bag of rice for a few days. Then mix up some slow-cure resin (thinning it isn't a bad idea either), and submerge the piece to be stabilized in a bowl, then place in your bell jar or whatever other vacuum vessel you've come up with.
As you pump it out, you should see bubbles in the resin itself, as well as coming from the piece to be stabilized. Once the bubbles slow to a crawl, you can vent the chamber and remove the part, and allow it to cure. You definitely want to use slow cure, because it will have less chance of putting stress into the workpiece.
Anyways, sounds involved, but when working with something that expensive, it's not a bad idea. There are companies that specialize in stabilizing too, so you may want to invest in that if you don't want to tackle it yourself. There are other ways to stabilize besides Epoxy resin, also.