I can see reasons why you would prefer that but in reality it is not a form of reparation. It would only be a form of penance.
Most companies do not have the capability of accepting donations from random, anonymous individuals. A cashier will be in as much trouble if $100 extra shows up in the till as if $100 is missing from the till.
In order for a store that uses any kind of an automated inventory system to be able to accept that kind of reparation is if the OP was to be able to list the inventory items by barcode and quantity and provide the payment (with tax) that corresponds to the price of those items. If, hypothetically, he was able to do that, then the store could manually enter the barcode and quantity into a POS terminal and then put the money (money order) into the till. Barring that, the store’s (chain’s) accounting department would be able to do the same thing.
But the OP said he didn’t have the barcodes for the items any more. So therefore, there’s no way to process the transaction and to account for the cash. A manual Journal Entry just randomly adding $100 to their books would be looked at VERY suspiciously by corporate auditors.
The bottom line is that when the store(s) do(es) its next periodic inventory verification, the items will be identified as shrinkage and their costs will be written off of the store’s income taxes. Even if it could happen, a journal entry adding $100 to the books won’t change that.
So actually going and restoring commutative justice is next to impossible…the only possible exception is a mom-and-pop that still does books manually without benefit of an automated inventory system…then, if the money order (or cash) got to one of the principals, it would be possible for them to make a manual journal entry. But that’s just about the only way it could happen.
If you’d like to test that theory, the next time you’re at Walmart, Target, or some other corporate store, go up to the customer service window and try to give them $5. Tell them your son/daughter/grandson/granddaughter/niece/nephew or whatever owned up to stealing a couple of candy bars and you wanted to make it right. They will praise you, thank you, comment that they wish more people were honest like you, and so on…but they won’t take your money (unless you actually have the candy so they can scan it).
I did so with a nefarious nephew several years ago who actually lifted some candy from a Wally World…and bragged about it at home. I wanted “to teach him a lesson”. I had him in tow so that they could appropriately reprove him and so on. And that’s exactly what they did (along with a fatherly, “have you learned your lesson, son?”)
When I came to better understand how accounting systems worked a few years later, I understood why that happened.
So knowing that there is not too much way for commutative justice to actually be restored (except in certain very specific instances…), the next question is: how does one endeavor to restore the right order of things. As I said above, there’s not to much way that one can, in today’s computerized world, restore the damage to the other party, at least the OP could make sure that there is no benefit on his end from the illicit commutation. At least he doesn’t profit from something immoral.
And the purpose of restitution is to restore commutative justice.