Most of the transmission is the same but the 126/SD has an inductive drive for the speedo while the 123/D has a mechanical/gear drive for the speedo. Apparently it's a lot of work to open the tail housing to swap parts. Might be easier to put a 126 speedo in your 123 cluster if it's possible.

The transmission numbers are a guide. I got my 81 SD (sold) with 290K miles. The transmission was a 722.309 out of a 280E but with a 126 tail housing. I replaced it with a junkyard 722.315 out of a 300Dt also with a 126 tail housing. Someone out there's rebuilding transmissions and using any old case.

Sixto
91 300SE
87 300SDL
83 300SD