Hi,
I've not saved seeds of them, but they are related to tomatillos and I'm assuming seed saving is the same. The seeds need to be extracted from the fruit. The link below is about tomatillo seed so do the same for your chinese lantern fruit.
Please let anyone you send seed to that this plant can be quite invasive in the garden and hard to eradicate so plant with caution or in a container.
Remy

Here is a link that might be useful: Tomatillo Seed Saving