well you've got a great answer here already.
Use a cut away stabilizer and a temporary adhesive hooping the silk in the hoop together with the stabilizer. Silk is very slick and will slide around if not stabilized properly. (I sometimes pin also just as an extra precaution.) Use a sharp needle. I use a 75/11 but you will need to do a test using the final design that you chosen. You may need a smaller needle, but be sure that it is a sharp. The ball points will push the fabric down as the needle goes down and cause you not to have a smooth finish. You may also find that you need to slip an extra piece of tear away underneath - again, depending on the density of the design you have chosen. Hope this helps.;)
I think it's a great advice you gave, ***for you both!
Interesting. I've never embroidered on silk but assumed you wouldn't hoop it for fear of hoop burn. Maybe not :)