IEJ vol. 9 #4 (1959, by Israel's Dept. of Antiquities back then) noted that these fragments were found in the Area A street south of the building in stratum VII; 3 of the 4 handles have "LMLK HBRN" stamps.  In 1973's "Beer-Sheba I", Yohanan Aharoni reported that the handles have 4-winged icons.

However, the entry for Tell el-'Areini in the 1975 edition of "Encyclopedia of Archaeological Excavations in the Holy Land vol. 1" states that this jar was found in Stratum VI "near the eastern building on the pavement of the lane", & that each handle was "stamped with the impression lamelekh/Hebron above & a 4-winged scarab below."

The photo below is from the 1973 English edition of "Inscriptions Reveal" by The Israel Museum, which also says there are stamps on each handle: