To reorder a Budget Item on the iPhone app, simply tap and hold the item you want to move, and drag up or down to change its position.
Unfortunately, at this time, we don't have a way to move a budget item to a different category/group, since a lot of the built-in reporting (included in Ramsey+) is based on group distinction. You would be able to create those items with the same name in a new category if you wanted, however, the data would not transfer.