These items were shipped through the mail and were not refunded through the Defense Travel Service.
Yes, as a Military member, you can claim Moving Expenses.
Military personnel should use Form 3903 to report their moving expenses:
If you’re looking at your W-2 to verify these amounts, the amount you report on line 4 should appear in box 12, code P. These directions are also included on Form 3903.
If your reimbursement exceeds your total out-of-pocket expenses, you won't be able to deduct your moving expenses, and you'll have to claim the excess reimbursement as taxable income. But if your personal expenses were more than the amount that you were reimbursed, you can deduct your out-of-pocket moving expenses to reduce your taxable income.
Here's more info on Form 3903.
Thank you for your service!