Why companies do this I have no idea !! Its not like anyone really cares !! Here is what I found,, There is no record of any company named Ammore,,, there is one named Amore that did make some childs size china !! Mizuno Pro is an American made baseball glove by company of the same name,,Mizuno International I think it said !! There is no Picky and Bobby but there is a Pinky and Bobby that I found although I think that Bobby may have been the creator of the video I saw !!
I have seen things like this over the years although usually they use a well known company name !! Your cup and saucer was likely made in any of the places that produce usually small souvenir type sets !! Their reason seams to be that with something like this marking it will sell better !! And certainly can`t be traced back to the actual mfr with the incorrect spellings and companies that do not exist !! May have been more info on the box if it came in one !!
This was common back in the late 60`s and into the 1980`s !! Of course there were no/ or few computers to check if they were correct or not and really no one cared,, it was not that important !! Then into the 1990`s when computers were more accessible people started checking on this stuff, and selling on the internet, you saw fewer and fewer marks like this !! What you find now are usually from that era !!
It is not a fake or a copy but rather a type of marketing strategy to improve sales for their product !!

Tell me everything that is on the back !! Can`t read the paper below it,, this site does not enlarge pics !!