Tim, First off, the buffer spring.
The difference in is between Rifle length, or carbine length, both the spring, and the buffer it's self are different.
(want to buy a rifle length buffer and spring ? )
Second, Armalite.
pretty much everything about Armalite is proprietary, Your SIL would have been much better off going with DPMS since their AR internals are pretty much one size fits all, less expensive, and have a much better chance of being compatible with other "AR" after market products.