Are the Skandhas reborn from moment-to-moment? Imagine a human being born in 1982 weighing a few pounds at birth and labeled 'Melinda' by her parents. This little human being grows up - as little human beings tend to do - and by 2020 we imagine her as an adult no longer called 'Melinda', but rather change her name to 'Abigail.' If we examine the bodies of Melinda and Abigail down to the atom and perform a thorough and exact accounting we find that Melinda and Abigail do not share even one atom in common. Their brains are composed of entirely different atoms. 

Is the rupa skandha of Melinda and Abigail the same or different? Has it been reborn? What was the manner of its rebirth? How did it occur? How many times did it occur between 1982 to 2020? Is the same true of the other skandhas... have they been reborn? Are they reborn due to 'identification' with an 'I' or due to physical laws or some combination? 

Did 'Melinda' die sometime between 1982 and 2020 and get utterly annihilated? Was Abigail born for the first time from scratch between 1982 and 2020 and just pop into existence from nothing?

How is it possible that beings are reborn from moment-to-moment? In what manner and to what extent? What did the Buddha teach?
Imagine a camp fire that started in 1982. The original fuel has burned down but new fuel is regularly added. The overall shape and configuration of the fire in 2020 is somewhat reminiscent of the original 1982 fire but of course none of the material is the same.

Now if we were to analytically separate the fire into several categories (skandhas) we would find wood, ash, heat, light, oxygen, and smoke - all playing their roles in the maintenance (upadana) of fire.

Is it the same fire staying or is the fire "reborn" moment to moment? It's neither and both, these are just concepts to explain the working of causal continuity.

One important mistake in the worldview underlying your original question:  it assumes that "the fire" starts when a new human is born. But this is not so. The fire has been continuously burning through generations. "The beginning point is not evident". A new human is just another tongue of flame.