I also had a Leica II which was upgraded to a III which also had the flash synch fitted later on or when converted to a III.
I talked to a well known technician when having it overhauled and he told me that this was a common thing in the past.
Films were quite slow and you wanted to tke pictures indoors so you wanted to use a flash, hence the upgrade.
Judging from what I can see, the camera seems to be genuine, Contax have the levers for unlocking the back in these terraced cones or however you want to describe it,
Kievs also had these but only in the early models.
Contaxes also almost always have the serial number on both the lower part of the inside body and the back.
But, sometimes, this is not the case.
Maybe that helps.