350 CE transmission swapped to 350 BB

[prepper]

I have a diesel 350 BB with first gear bad, will a 350 CE transmission interchange into the BB?
the serial number for the BB is 183160 T
the serial number for the CE is 328267 T
Transmission on the bb did not come with a reverse gear
I have not pulled the transmission as it still works in 2nd gear
I am going to change both steering clutches and would like to fix the transmission while it is down
I am aware the CE has wet clutches and mine are dry
BB has power steering if that matters
I have the CE transmission lined up for $1800.00

[Lavoy]

I may be wrong, but I highly doubt it due to the wet clutches and associated oil flow through the housings.
lavoy

[prepper]

I see that the input shaft and gears are the same according to the applicable models of b-c-d so would internal parts be interchangeable?
or
Any lead on how to get parts and a manual to put in new first gear?
or
Working transmission?