Danish census in 1885 was taken in February? I suppose in that case he could return to the USA anytime after the census that February of 1885.
He could be in the USA two years and then file "Declaration of Intention to Become a US Citizen", then be eligible to receive citizenship three years later, in about March 1890 - a five-year process total.
See Naturalization Process,
In any case he certainly could have been a US citizen in Feb 1901 when he was living in Denmark.
I thought the record I noted and you opened was a request for a copy of papers that had been previously received, but lost.
I suppose he could have died before the 1910 census - among other possibilities.