In my personal research notes, I found my summary of Special Order #87 issued by General M L Smith:

6/17/62 S O #87-Smith
-Lt Pinckney, T, F. Co cdr in 8th La Bn Arty assigned to duty by Smith
-report organizations perfected
-Herrick assigned to duty.
-Capt Tissot assigned to duty [23rd afterward 22nd La]

A previous order issued by Smith related to these same units as follows:

6/1/62 Hqs Vicksburg, M L Smith issues S O #84-
Maj Gen Lovell cdg Dept having directed the consolidation & reorganization of the Co’s of the Regt of Hvy Arty-Col A. Jackson, Pinkney’s Bn, 22nd & 23rd Regts of La Vols, the following consolidation is now in effect:
I. Regt of Hvy Arty consolidated to 4 Co’s from 10 to be known as Col Jackson’s Hvy Arty Regt
II. The 22nd La is consolidated from 4 to 2 Co’s
III. The 23rd La is consolidated from 7 to 3 Co’s including Capt C Herrick’s & Capt Tissot’s Co’s. Maj Ogden cdg.

As you may know, these were fragments of units that had escaped the New Orleans surrender that had congregated at Camp Moore for reorganization. Before that could be perfected, General Smith was hurried to Vicksburg to expedite the arming of Vicksburg's defenses. These were some of the units that were sent there by Smith to man the heavy artillery batteries being constructed.

Smith himself arrived at Vicksburg and assumed command on May 12. 1862. At that time Gen Smith stated: ...the state of preparation for defense was as follows: Of the ten Btrys that have been in use three were mostly completed & a fourth begun; the armed troops present consisted of the remnant of the 8th La Bn, Lt-Col Pinkney, & the 27th La Vol, Col Marks, both of my Bgde, which had preceded me some 6 or 10 days. Col. J. L. Autry, ordered here by Gen Bragg, was found in command, pushing the works forward vigorously through his chief engineer, Capt. D. B. Harris, who afterward remained with me in the same capacity until most of the works were completed.*
From the 12th until the 18th the works were pushed forward night & day with all possible vigor, at the end of which the first Div of the Federal fleet, together with transports carrying some 3,000 men, made their appearance, & found us in a condition to dispute with a fair prospect of success a farther advance; that is to say, six Btrys were complete, the gunners at their posts & fairly drilled.

Smith also began the process of rearranging the fragments of units as indicated by the Special Orders referred to. It was in that context that Lt Pinckney of the 8th La Bn [commanded by Lt Col Pinckney]was assigned to duty as were other officers of similar commands.

Lt Pinckney's consolidated service records [see Fold3] shows that he subsequently signed receipts during October and November 1862 as Lt, cdg the 1st Co of the 8th La Bn