John Singer Sargent said, "A portrait is a painting with something wrong with the mouth".
“A portrait is a painting with something wrong with the mouth”
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He was, after all, a Sargent, and thus out-ranked Homer.
I gather that you have already decided that this is an image of Grant. The original post suggests a high degree of confidence that this individual was a soldier from Alabama. We should ask why. Several Alabama uniforms from the early Civil War period have been illustrated which show a somewhat similar button pattern but without the shoulder straps. The columns of buttons on the uniform illustrations do not all appear to be straight up and down with top-most buttons up on the shoulders. Is the uniform depiction accurate? As indicated, the illustration is not made by a gifted artist and the rendering of the uniform may be a point in favor of interpreting the illustration to be of Grant.
There were hundreds of thousands who served during the Civil War. Similar hair styles and physical appearances are bound to have occurred. On the other hand, depictions of Grant must have been freely available both north and south for an artist to try and copy. If this is a painted-over photograph, it's interpretation might be much different than if it is a painting or pastel sketch.
I think we need more information about the portrait and why the original poster feels the subject is from Alabama. Does the original poster have an idea of the subject's identity? Until we know more, anything is possible.