Very interesting! We just have to make a timeline. By the way, with the limited resources that I have available, I have found that 2 persons who were present when Mathew made his pension applications were in the 37th Mississippi. In the July 1916 application, A. L. Mceachern was with Co E of the 37th, and in his Sept 1921 Application Jas. B. Evans was in Co. E of the 37th.
We do know his next child with Jane was not born until about 1868.