First military move! Help!?

If you are on his orders (which you usually aren't unless you were married prior to him entering Basic) then they will move your stuff. I am uming you have the majority of the stuff, and he just has personal items. If you are not on his orders, you are responsible for moving your own things. If he is graduating AIT in 3 or 4 weeks, he should already have his orders, If you log into his AKO account, it should be listed there already.