6A13TT comes with AWD gearbox and its not a simple job to swap over, slapping a FWD auto gearbox on it will result in a burnt out gearbox after a few hundred kms. - regular FWD manual box will suffer from massive clutch slip when those turbos spool up.
I have done a lot of engine swaps on these cars and the engines of choice were
6A12
6A13 NA
4G63 - Right side mount
4G93 - NA - not GDI type (right side mount)
get a bone standard automatic gearbox and mount it with the engines, make sure your wiring is A spec and complete - you will have to splice into the fuel pump circuit, gauge panel and also some interior bits - you will need to trim down the replacement wiring if the one you buy is from AWD.
Its easy if you are versed with mitsubishi build system and wiring schema.
Dewan Motors sold this Galant with a 4G63 carburettor engine, its also a good choice if your car has a lot of bits n pieces missing or burnt away.
word of advice (freindly one)
If you are dreaming of a tire smoking car to impress the ladies and plan to do a 6A13TT swap and expect it to be reliable and workable in any economic sense then its better to stop right now and buy something else like a sports bike (ladies love a dude on a sports bike)
The VR4 Galant is not your regular run off the mill Galant. Its very different underneath.