In 64 Fairlanes, there were two 6's (170 and 200). The 170 used a light duty trans for that engine only. For the 200 and the 260/289's Ford used what is called the 3.03 trans.
Since the 144 is the same casting as the 170 and 200, the 3.03 trans should fit. I don't know if the light duty trans had the same bellhousing as the 200 though ( transmission bolt pattern wise). You may have to use the 200 bellhousing.
I don't know if this was the same in 63 and 65. Logic tells me it is so, but Ford sometimes did not seem to use logic at times.
The 3.03 trans was used in lot of cars in the 60's.
I don't have any info on input shaft length or splines.