I'm not a philosopher, so this response will be imperfect and is subject to revision.

Then why do you think that the perceived continuity of having an ego is a real thing that exists?

My current response to this is that something can exist without being made of something. Consciousness is an emergent property of a sufficiently complex, chemically active neurological system. (Someone can poke holes in this definition if they like, but come on dude, principle of charity. You get what I mean.) Essentially, "how it feels like to exist" is a real, if immaterial, thing. Just like mathematics and language.

If someone makes a perfect copy of my brain and body over by the lever, using none of the materials from my original body, then it is a different brain and body, no matter how arbitrarily similar it is. The consciousness that was by the entrance to the teleporter will never experience pulling the lever.