I am sorry that you have had this trouble. Unfortunately, the Tax Cut and Jobs Act of 2017 eliminated your ability to deduct theft losses, which would have been the normal way to take a deduction for the loss.
The IRS tax code does not address the situation of theft in an HSA and I can't recall that any IRS Notices address this situation, either.
If you do get reimbursements for these amounts, please have a talk with your HSA custodian, because you DON'T want these amounts reported as contributions to your HSA. That would foul up the reporting to the IRS. Instead, ask your custodian if they can simply replace the stolen amounts as the return of mistaken distributions (which means that they will have to convert all those fraudulent distributions to mistaken distributions).
So make up a list of all the theft/distributions, so that if the money comes back, you can give them a definitive list of which distributions need to be recharacterized as mistaken distributions that you will "pay back" with the reimbursed funds. Go ahead and talk to your custodian now to see if you can get their agreement to do this.
In that case, you won't have to do anything else.
