seems that either you've got an other mount on your AF-B than I or that the 5D-c has a different mount-shoe for the eye-cap than the 5D-III.
Here is a picture of my AF-B in total plus it's mount next to the mount-shoe of my 5D-III.
I hope that someone just could tell me "buy the 'Adaptor xxx'" or so :-)
I owe you an apology. Upon closer inspection, it is actually apparent that my Angle Finder B seems to have been 'hacked' by a previous owner.
A few weekends ago, I stumbled upon a new in box AF-B; it looked like it had never been opened. So I bought it, took it home, and tried it. It fit my 50D, but not my 5D3. WTF.
Then I got out the calipers and did a close inspection of the one that does fit. The metal mounting piece is clearly different...then I noticed that two screws were missing. Humm...what's this?
It turns out that the mounting piece from an Angle FInder C (the adapter part "Ed-C") just happens to have a hole though it EXACTLY the same diameter as that of the AFB. And two of the four holes for the little phillips head screws line up.
So the solution to using an AF-B on a 5D3 is to buy an Ed-C from Canon (less than $20 delivered), take the mounting piece off (four size 00 philips screws), remove the mounting piece from the AF-B, and put the piece from the Ed-C on. The screw holes in the opposite corners will line up perfectly (lower left and upper right when looking at it).
I am quite ashamed that I hadn't noticed that before, so again, my apologies for misleading y'all.