how would you explain rebirth to a non-Buddhist who believes in an eternal soul

https://buddhism.stackexchange.com/questions/49086/what-is-it-that-pass-from-this-life-to-the-next/49154#49154

>>how would you answer this question so that it can enlighten/delight/pacify someone from a non-Buddhist tradition (with some inclinations towards an eternal soul).

If you develop samādhi (undistractible lucidity perfected with meditative training) to a high level, you can witness for yourself what happens to a soul at the moment of physical death.

If you don't (develop samādhi), then all you have is just hearsay, beliefs, and views.

Yogis with developed samādhi from all religions, Hinduism, Taoism, Essenes, christian mystics, etc., all witness rebirth of the "soul" as a real observable phenomena.

The difference with the Buddha, was he found that the "soul" is conditioned, impermanent. 

With proper understanding and training, 

one can bring an end to the infinite cycles of rebirth and understand what a "soul" really is.