There are two Cadillac 390s. The original postwar overhead cam V8 331/365/390 will not mate with a TH350 or TH400. They used the Hydramatic transmissions.
This engine's successor was a completely different 390 - the precursor of the hated Cadillac 429. It was introduced in 1963, whereas the TH400 debuted in 1964. The '63 390 still utilized the old Hydramatic transmission - Jetaway on Oldsmobiles.
The 1964 Cadillac 429 utilized the TH400.
I'm not aware of any adapters available to mount a TH350 or TH400 on an engine originally equipped with a Hydramatic.