Thank you for your reply.
The Contax IIa body in the picture you posted is a early, black dial version. The serial number starting with a P is entirely consistent with the look of that body.
As I wrote in my posting, on mine, the S/N is also engraved inside the body. I can see that when I take off the back. The S/N engraved inside is the same as the one on the accessories shoe. It starts with a T, which is inconsistent with the technical layout and looks of my IIa.