Morton Pension Index card lists his date of discharge from Co H, 1st Mo Engineers as Sept 14, 1864
see: https://www.fold3.com/image/5758550/morton-charles-us-civil-war-pensions-index-1861-1900
It also lists service in Co I, 25th MO Infantry see Baker below. No doubt in my mind these 2 knew each other for an extended period of time, trials, and tribulations, i.e. brothers in arms. So yes, the dates work.
He transferred from 25th Mo Inf to 1st Mo engineers Feb 17, 1864
see: https://www.fold3.com/image/5438127/morton-charles-us-civil-war-pensions-index-1861-1900
see: https://www.fold3.com/image/231852180/morton-charles-page-3-us-civil-war-service-records-cmsr-union-missouri-1861-1865
He apparently was an orderly in brigade headquarters while in 25th Mo Inf. Born in Cuyahoga Co Ohio. Enlisted 1861 as 16 y/o 5'8" fair, brown hair, blue eyes, in St. Joseph MO enlisting in 13th Regt MO Infantry.
See: https://www.fold3.com/image/231852196/morton-charles-page-19-us-civil-war-service-records-cmsr-union-missouri-1861-1865