Depends on your beliefs and what you define 'us' as. Will a conscious being be born after you die? Yes. Will it be 'you'? Probably not- as far as we are aware. Do you remember past lives?
I consider 'us' to be unique- in terms of- we were born to a specific set of parents at a specific time and location. Unless there are billions and billions of earth's out there to account for the billions of timelines, all running the same story, how else could you be born to the same parents, inherit the same genetics etc?
If you had different parents, if you were born 3000 years into the future on Mars. If you were born as a whale- would 'you' really be 'you' anymore?
It depends how you view consciousness I suppose. Whether you view it more as an independent entity that can float in and out of beings or, whether it's something more akin to an ability- like sight or, hearing. I personally believe our brains generate consciousness for the time period we are alive. Sure- other brains will exist in the future that generate their own consciousness but, I doubt they'll have anything to do with what I recognise as 'me'.