Don't try to solder near that pearl. It almost certainly will be damaged!
Moby pearls are usually assembled from a hollow hemispherical shell of pearl with a relatively flat cab shaped mother-of pearl back and a plastic or resin core. Heat of almost any amount that is too hot to hold for more than a few seconds will cause the resin core to melt and expand and become unglued. Soaking in acetone or other chemical is likely to create the same result. Damaged Moby pearls are all but impossible to repair.
It is possible to remove the pearl from the setting, but extreme care is necessary. I would first make sure that the pearl isn't tightly set by the bezel, most likely it's not, Then I would grip the back strap of the setting with hot tweezers right at the post that goes into the pearl and twist on the top of pearl gently with bare fingers. But I've done that kind of thing many times before, so I know what it's supposed to feel like when it's getting close to either loosening up or burning up.
If you're not familiar with this technique of ungluing pearls, I'd defer that portion of the job to someone that is. After that, you can make a shank and solder it on like you would normally do, and re-glue the pearl. Or you could do it really right and set it using the bezel, but remember that the pearl hemisphere is hollow with a plastic backing and not very resistant to damage.
Whatever you do with that pearl, It's probably going to be risky no matter how you do it, so a conversation with the owner concerning the risk is highly recommended prior to any attempting work.