A plant keeps its number and all its data when it moves. Both lifecycle dates are kept as well: the date of placing in a box answers the question of when germination ended, so a move does not change it.
You CANNOT see a LIST of a plant's previous moves in the app: there is no such screen yet. The plant card shows only the two dates - germination and placing in a box. The moves themselves are recorded and are not lost, but there is nowhere to show them right now.
After a move to ANOTHER box the screen opens the original box again: this makes it convenient to move seedlings in batches without going back through the box bar every time. The destination box stays next to it in the bar, one tap away.
The notice about a successful move names both the destination box and the cell in it: «Moved to box B4, cell A1». The box is named because by that moment the screen has already returned to the original one, and a cell address alone would read as a coordinate of the box in front of your eyes.
A move inside one box does not switch the screen, and the notice there is short - the cell address only: the box is the same, there is no point in naming it.