If an Animagus transforms to their animal form, can they pack their wand such that they get it back when they transform back to human form even if they travel far from where they have transformed?
I don't recall any example in canon that would decide this. We see McGonagall untransform in Stone chapter 1, but we don't learn whether she has a wand with her. Neither Sirius nor Wormtail have had a wand of their own during the events of Prisoner, and we rarely see them transform in the later books. Sirius transforms during Goblet when he goes to the railway station, but does not untrasform until he returns to the Headquarters. Rita Skeeter presumably never untransforms in Hogwarts, because of the risk of getting caught.
One relevant event is when Lupin transforms to a werewolf in Prisoner chapter 20: he drops his wand. However, Lupin was unprepared for the transformation at that time, and maybe he could have “packed” the wand if he prepares to transform. Besides, the rules could differ for a werewolf and an Animagus.
See the related question What determines whether or not an animagus can retain their clothes? which explains that we believe an Animagus can keep their clothes at least, and In HP Goblet of Fire.. How does the Body of Cedric Come out of Voldemort's wand when he was killed by Wormtail? where this question has come up.