Particle System teleport: How?

Is there a way to teleport an entire particle system, including previously created particles, without losing them, even though they’re originally created in world space?

I don’t know if it’s the best way to do this but you could simply change the position of each particle using GetParticles and SetParticles

Yes. As you want to move not just the position that new particles are emitted from but also all existing particles, change transform.position of the game object that has the particle system.