Mr Klinkel said he collected fragments from the droppings, and his daughter, who he was visiting in Denver, later found more when the snow melted.
Mr Klinkel, from the town of Helena, washed and bleached the remnants of the bills and sent them taped together to the Treasury Department in hopes of having them replaced.
That process could take up to two years, Mr Klinkel told the Independent Record, the newspaper he works for.
"Sundance may have eaten my money, but what he took he gives back in unconditional love," he said.
Mr Klinkel also told the paper he was embarrassed by all the attention he had received.
"I got a call today from a guy I knew 20 years ago and he said he hasn’t stopped laughing about it," he said.
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