If "Albert Johnson" had served un the US Army during World War One (1917-1919 time frame) he would probably be listed in the Adjutant General records of Washington state.
Those records, which can be searched on line, contain rosters and abbreviated service records of many who served in the National Guard and National Army.
Unfortunately, there are over a dozen Albert Johnsons and a dozen Arthur Nelson's listed. And both names could have been simply aliases used by the "Mad Trapper".
However, this resource might be of interest in looking up other possiblities.
Those records, which can be searched on line, contain rosters and abbreviated service records of many who served in the National Guard and National Army.
Unfortunately, there are over a dozen Albert Johnsons and a dozen Arthur Nelson's listed. And both names could have been simply aliases used by the "Mad Trapper".
However, this resource might be of interest in looking up other possiblities.