actually US iphone also have 'LL' model number

and real refurb phone have '5k' as two starting letter for serial (note:serial not model number)

so my take is 'LL' are same as those iphone in black box which apple store in US used to swap out defective phone.
Genius in apple store US claims those phone in black box are new.

My theory is apple made those new iphone in black box to quickly replace defective phone without needing to replace cable/earphone/printed thingy to save cost.