Well, that's a good question. Short answer, probably not very well. I don't use H/S stocks so forgive my earlier ignorance/answer.
CA (superglue) usually doesn't lend itself well to foam. There is foam safe stuff but it's not very good-especially for something like this.
I'd probably go with an epoxy. Something thin so that it'll wick into the foam's pores. Paint a layer on the foam, allow it to cure, then sand/machine it flat again, and then glue your pad to it. This way you have a hard/similar surface for the resin to bond to.
Ureathane glue ,will stick very well,easy to use ,no mixing, you will be shocked at how little you use,just masking tape the exposed edges of the stock and pad at the joint. Your tuffest job will be securing the pad to the stock as the glue cures..
When doing the foam filled fiberglass stocks, I hollow out the stock about a half inch deep, and then fill with a 2 part epoxy and level off. After it cures I put it on the drum sander to get a perfectly flat surface. then the new pad can be screwed to the stock, scribed, taken off and rough ground. Then installed with the screws and a thin layer of epoxy, and finish sanded to fit flush.