Sharon Fruit are now a major export of Israel, which might lead you to think the name is somewhat biblical, along the lines of "Rose of Sharon" and all that. The fruit was, however, actually developed in Japan as a variety of Persimmon.
Sharon fruit looks very much like a persimmon; the difference is that you can eat it while it is still firm without your entire face puckering up on you, as it would do with a firm persimmon.
No need to peel, just wash. The skin and the core are edible.
Wrap individually and freeze for up to 3 months; when thawed, use for sauces.