Yes the military will move your gear for you. You will need to pack it up and load it on the trucks TMO (Travel Management Office) will then transport your gear to your new home. You will then offload it and they will pick up the containers. I personally am not sure of the details as I have never let the government move me. Something about trusting my life posessions to strangers...
You can also do a DITY (Do It Yourself) move. The government pays you a certain maximum amount to help cover costs to move yourself. This is usually based upon rank. They give you so many dollars for so many pounds. I did a DITY move from LA to NC. The government paid me $1500.00. I used that to pay for the moving truck, gas, packing equipment, overnight stay in a motel room, food on the road, and cleaning supplies and such for the house I moved out of and to replace the perishable food items.
This at least is how the Marine Corps does it.
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