Corydoras experience the world as a group. A single cory in a bag is a frightened fish; the same fish inside its shoal is merely an inconvenienced one, and that difference decides how well they travel. They are also built close to the ground: whiskered barbels that taste the substrate for food, soft bellies, and a habit of resting together in a loose pile. A move that respects the shoal and protects the barbels is a move they shrug off within days.
A shoal moves as a shoal
Pack the whole group into one roomy, sturdy container of their own tank water rather than splitting them into individual bags. Roomy is doing real work in that sentence: corydoras under stress in tight, crowded water are known among keepers for fouling their water unusually fast, and volume is the buffer against it. Fast the group for a day before the move so the water starts clean. Add nothing sharp to the container, no rocks or rough decor they can be thrown against when the car brakes.
Set up sand and shelter at the new home first
Prepare the destination tank before they travel: a soft sand substrate rather than coarse gravel, because corydoras sift sand through their gills and worn, eroded barbels almost always trace back to rough or dirty substrate; smooth hiding places and plant cover at floor level where they actually live; and water at their settled temperature, broadly the low-to-mid seventies for most common species. Move their filter media wet in tank water so the bacteria colony arrives with them. If their old tank had a particular cave or leaf litter corner the group rested in, recreate its position; corydoras return to a familiar resting spot like commuters to a platform.
Travel steady, then settle them together
Keep the container dark, level and in the car cabin, where temperature holds steady. On arrival, acclimate gradually by mixing new tank water into the container over half an hour or so, then release the group together and leave the lights low for the rest of the day. Offer a small sinking meal that evening; a shoal that descends on it together is a shoal that has landed well. Over the first week, watch for the specific corydoras warnings: one fish sitting apart from the group day after day, barbels looking shorter or ragged, or rapid breathing at rest. Check the water readings first if you see any of them, and contact an aquatic veterinarian if a fish stays isolated or the breathing does not settle, since barbel erosion and breathing trouble can point to water or bacterial problems that need prompt advice.
With KinsLe Family Sharing, the shoal's numbers, their sand requirement and the first-week watch list sit on their shared profile, so the person who reaches the new house first sets up the tank floor the way the corydoras actually need it.