We can save you trouble there. The service record and Georgia pension application show this man's first name to be Simeon. The only Solomon Fuller in Confederate service is listed with Hoskins Mississippi Battery, AKA Brookhaven Artillery. This man appears on the 1850 census as a resident of Marshall County AL. He married Louisa Payne in Shelby County in 1857, doesn't appear on the 1860 as best I can tell. However, he and Louisa are in Waco TX in 1870 and have two children ages 12 and 10 born in Alabama.

You might do well to check into a Texas pension application. If he actually served in the Confederate army and was eligible when pension legislation was enacted, he should have applied.