As someone who once returned over $20,000 in jewels to a Sri Lankan diamond trader that I found in the back of a Bangkok taxi, I am a fairly honest person.
However, finding cold hard cash with no immediate way to trace the owner available? Hmmmm that's a tricky one.
I generally make sure my ID or contact info is available in all my travel items should I lose them.
In this case I think you should keep it. The owner didn't appear to make much effort to hang on to the cash.....
Just MHO!