They moved on from Muzdalifah at the end of the night, and stoned the Jamrah and did tawaaf and sa‘i before Fajr

What they did is permissible and there is
nothing wrong with it, because if it is permissible for a person to move on
from Muzdalifah, it is permissible for him to do everything that follows
that. So if they move on, for example, from Muzdalifah  at the end of the
night after the moon disappears, and they reach Mina, then they may stone
the Jamrah and go down to Makkah to do tawaaf (circumambulate the Ka‘bah)
and sa‘i (go between as-Safah and al-Marwah), and  come back. And if they
come back before sunrise, there is no problem with that, because it was only
made permissible to move on (earlier) for those who are weak so that they
would be able to do the rituals of Hajj before the crowds of people became
very great. End quote.