Can you tell by looking at this who the thieves are who stole money from my mother's bank account?

You are the most unusual person on here.

And on Answer Bag.  I don't know anyone like you.

Tell your mom to call her bank. They'll research it and if it's fraudulent, they will reverse the charges. 

I just read an article saying that businesses, especially gasoline stations, are putting a hold on as much as $125 when people use debit cards for gasoline.  That money may not be accessible to them for up to 48 hours.  That is ridiculous and is going to require some legislation.  Some convenience store association created this protocol.  Call your congressman.

Call the number listed with the transaction.  That is who got the money. Not necessarily who committed the fraud. But the company the crook used her card to buy something from. 
Call them and tell them it was fraud, they will likely simply reverse the charge.  If they refuse call the bank and they will likely reverse it but will require you to call them yourself first.