On a regular basis I see ads on eBay where a Leica II is offered as being a Leica 1a. If you study the serial number then you would see that it is a 1a. How did that happen?
If you would send your Leica camera to the Leitz factories for maintenance or repair, in the thirties, you would automatically get some new features.
Already from the introduction of the Leica II in 1932 it was possible to have the earlier models to a camera with interchangeable lenses and a build in rangefinder (Emmermann page 171 Jahrgang 1 March-April 1932).
The serial number would stay the same. In many cases the top plate had to be replaced, then the serial number had to be engraved again.
Therefor it is very well possible that an early Leica 1a is converted to a Leica II, III or even a IIIa with a very low serial number.
A Leica II could be converted to a Leica III or IIIa as well.
If you wanted to convert from an 1a with its fixed lens, then the whole lens mount had to be replaced and the lens itself had to be changed in that it could be screwed of the camera.
Apart from the conversion of the camera’s Leitz also offered to supply a lens with a rangefindercoupling. Then one could use cameras with a rangefinder to the full.
A black camera stayed a back camera in this process. Although exceptions exist see https://www.l-camera-forum.com/topic/276304-leica-i-a-in-chrome-finish/
An example of a major conversion is that of a 1c (Chrome, no finder at all and two accessory shoes, fastest shutter speed 1/500) to a IIIf with rangefinder a fastest shutter speed of 1/1000).
In my Leica documentation I have a pricelist from Leitz New York (Leica Camera and Lens Conversion Prices. This pricelist has no date, but it must be of 1950 or later as a conversion to the Leica IIIf is offered. Picture 2 and 3.
Conversion fro a Leica 1a is still offered in the fifties. The price for conversion from a Leica 1a to an Leica IIIa would cost 156 USD.
In picture 1 you will see an early Leica 1a conversion to a Leica III. Unusual is the fact that also the black enamel top and bottom plates have been converted into chrome ones.