Any idea what became of Brown's Battery following Marmaduke's December 1862 through January 1863 expedition through southern Missouri?

Battles
Brown's Arkansas Battery was assigned to Colonel Joseph C. Porter's Missouri Cavalry Brigade during General John S. Marmaduke's December 1862 through January 1863 expedition through southern Missouri.[8] This movement was two-pronged. Col. Porter led one column, comprising his Missouri Cavalry Brigade, out of Pocahontas, Arkansas, to assault Union posts around Hartville, Missouri. When he neared Hartville on January 9, he sent a detachment forward to reconnoiter. It succeeded in capturing the small militia garrison. The same day, Porter moved toward Marshfield. On January 10, some of Porter's men raided other Union installations in the area before making contact with Marmaduke's column east of Marshfield. Marmaduke had received reports of Union troops approaching to surround him and prepared for a confrontation.
Battle of Hartville
On January 10, Col. Samuel Merrill commanded an approaching Union relief column from Houston, Missouri. He and his command arrived in Hartville that morning, discovered that the small garrison had already surrendered. His force went into camp on Wood's Fork of the Gasconade River. Early on the morning of January 11 the approaching Confederates under Porter made contact with Merrill's scouts and skirmishing commenced. Marmaduke believed he was being pressed by several forces, so he diverted Porter and Shelby's columns along another road to Hartville. Meanwhile, observing this movement, Merrill marched his force directly to Hartville where it took a strong defensive position on covered, high ground west of the courthouse. Shelby and Porter's brigades attempted to dislodge Merrill's force, but it was too strongly positioned. Over a four-hour period several Confederate assaults were made, each being repulsed in turn. Eventually Merrill withdrew most of his force. Both sides claimed victory in the Battle of Battle of Hartsville. Marmaduke had united his force and secured his line of withdrawal. He set up a field hospital in town and could claim to control the field briefly, however, he was compelled to make a rapid retreat into Arkansas and then an arduous trek to winter camp.