Right click it for edit should highlight it as that is standard SL viewer object edit functionality. Once you have moved things into its contents folder it should show that it has items in the basket as it shows it with a clothing texture image instead of it been empty. It should be easy to select it and then take it into inventory.
When you recall a basket from archive you just add as it will wear as HUD.
Other than that, it would require Carlyle to make some changes to Archive for the basket to work differently.