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Lost,
I think you have identified your problem (and maybe just didn't realize it). You mentioned it gets full sun, but you haven't watered in three weeks. I say, the wrinkling is a definite sign that its begging you for a drink. You should water it more frequently during its growing season (when it dries out, water again). Hope this helps.

Planto

Yes, that is what a dehydrated Jade looks like :-)

Josh

Thank you guys so much! Will he recover? I watered last night.

Lost,
He may lose some of that foliage that is beyond "repair" but I believe it will be ok. I know you're new to plants, so maybe you could research jades online to better determine their care (sorry to direct you elsewhere but I don't know a lot about jades... Just watering when dry (will want to checkout when to water in winter, I believe they're spring/summer growers. Some succulents do their growing in the winter for example).

Planto

You could minimize foliage loss if watered at later part of day nites or very early AM or cooler days, a little less hotter sun but still kept bright..If fast draining mix for soil is in pot and location of the plant should be about a week for a complete recovered plant.
They're an opportunist plant growth will start as long as conditions are good enough for them to grow. It's usual to water less in winter to prevent stringy growth with the lack of sun. They tend to not want to grow in hottest temps during times of summer but would still need some watering to keep the roots cool as well as dehydrating.