I would like to replace my previous answer of Castle Picnkey with
Ft. Johnson. I guess the key word being "Prior". Since Maj. Anderson moved on December 26th and Castle Picnkey was the 27th, that only leaves Ft, Johnson.
While the fort continued to fall into ruins, an 1833 map reveals that the site had become a substantial facility for the US Board of Engineers. The facility included a wharf, two docks, a barracks, quarters for many staff persons, storerooms, offices, carpentry shop, tool house, blacksmith shop, a boarding house and many "Negro houses." Just to the southeast of this complex were the beginnings of the summer village for the James Island Planters. In time this village, called Johnsonville, contained many planters' homes, a church, commissary and a schoolhouse.
Source:
http://www.sciway.net/city/history/fort-johnson-sc.html
Edit - Your original answer of Castle Pinckney was correct, but unfortunately, I have to take Fort Johnson as your final answer. As indicated in the edit to post # 10, I consider that answer incorrect.
Note that the question asked about a garrison that was located at another fortification prior to Anderson's move from Moultrie to Sumter - it didn't say that that garrison moved to Sumter before Anderson did.
Hoosier