A transaction ID or bitcoin address alone will give you no clues as to what sort of wallet created the address that the bitcoin was sent to.
You will need to work with you mom to remember where the coins were sent. Try searching her digital devices for wallet applications, her email for wallet backups or exchange/wallet service registration emails, her ...
If you are known to own some bitcoin, then you might be expected to pay taxes at some point in the future, according to whatever tax laws you are subject to.
But if you outright lose your coins, then you probably won't be expected to pay those taxes anymore, as you 'won't be able to spend the coins in the future'.
This is more of a frame-challenge than a direct answer:
you only pay when you convert to fiat or spend the Bitcoin
I don't think it's nearly that clear. For the longest time, there was little to no official guidance on how Bitcoin would be classified as well as what sort of documentation and reporting would be required. Even now as regulators are starting ...