Hi, would a late Td5 / Puma rear door lock fit the early Td5 type door?

When l bought my defender l bought l puma lock set, as l just wanted the ignition key one to open everything, it worked but I couldn’t get it to work with the rear door.

I now have to replace the rear lock and l’m hoping that l can fit a new style lock.
I would appreciate any advice as l don’t want to buy the wrong lock.