I was collecting JSA from the post office a couple of weeks ago, and handed her €2 so she could give me my payment in all notes. Later that day when I was lodging it into the bank the teller told me that I'd an extra €10 and asked if I wanted to lodge it all. The lady in the post office had given me €10 too much. I went back the next day and handed it back to the same lady. She had realised her mistake soon after I'd left the previous day and was very grateful at my returning it.
To further rebutt the OP's opinion of a typical AH lurker; I'm currently back living with my folks. I buy all my own food, do all my own cooking, washing, ironing. I help with cleaning the house, mow the lawns and hand up considerably more than my share of the bills.
OP I hope you will reconsider handing the money into the guards. Someone somewhere is having a very stressful time because of losing that cash.