Why it was shared with the Soviet Union was basically because the Soviets were willing to pay for it - Christie sold two demonstration models and the rights to produce Christie suspension tanks for 10 years to the USSR in 1930. I had actually always assumed this was all above board, but apparently this was via a front company called Amtorg, which was set up by Armand Hammer, who is an interesting character in himself but tl;dr was something of a go between for Soviet business and the west.

It wouldn't have been that far out a notion for a western design to be used in the USSR, for example the ZIS-5 truck was developed with assistance from the AJ Brandt company and strongly resembled something designed by Autocar. Even during the Cold War Fiat built a factory in the Soviet Union.

As to why the Soviets liked the Christie suspension - it suited their armoured doctrine at the time. The Christie suspension was suitable for light, fast and long ranged vehicles. This fits nicely into the 'deep battle' doctrine which at the time the Christie suspension was purchased, was the next big thing in Soviet military circles. The Christie suspension was used for the BT series of tanks. When the Soviets were upgrading their tank fleet based on lessons learnt, they merged some of the 'calvary' tank functions of the BT-7 with those of the T-26 (which was intended as a light infantry tank), resulting in the now famous T-34.

This is where I read about Amtorg etc.:

http://en.wikipedia.org/wiki/J._Walter_Christie#Dealings_with_foreign_governments