Yes, you can make direct contributions to your old HSA by sending a check to the HSA administrator. This is called a "personal" contribution, and will appear on line 25 of page 1 of your 1040 as an adjustment to income. It's not quite as good as a payroll deduction because the payroll deduction not only doesn't pay income on the HSA contribution, it also doesn't pay Social Security taxes or Medicare taxes. However, in your case, it's a good second place.
Pass your payments for those medical expenses through your HSA, and you will convert the dollars that you pay those expenses from after-tax to pre-tax dollars.
