When I obtained my W113 it was fitted with a late W108 motor and automatic gear box. If I recall correctly, to retro fit the original motor and automatic gear box, the propshaft tunnel had to be reshaped (as the W108 gear box was wider and the tunnel had been widened), the gear lever gate opening in the tunnel had to be slightly moved forward and the propshaft had to be replaced.
The late model W108 automatic gear box would fit the W113 motor itself without any complications, the challenge lies the other necessary modifications.
Klaus