Using the Handle-Matching page as a guide, two H4C handles (#36 & #37) in the Redondo Beach collection have many similar characteristics suggesting they once belonged to the same jar:

• No incisions
• Same style of fingerprint-smoothing all over
• Purchased from the same IAA-licensed antiquities dealer in Israel at about the same time
• Same stamp quality (deep & with a depression-emphasis on the jar-side)
• Same stamp location (1.0" from joint to seal center; 0.4" from joint to seal border)
• Similar handle shapes (a triple depression forming 4 noticeable ridges)
• Same handle size (~9/16" thick; other parameters not possible due to #37's fragmentary state)
• Identical ware colors SGG
• Same sparse mixture of white grits
• Similar dirty patinas; spotty encrustation

Since both stamps have similar orientations (#36 is 12:30; #37 is 12:15), they were most likely adjacent rather than opposite on the jar.  The 2 photos below show them situated in alternate positions, with the loops as far apart & as close as possible given their fragmentary condition (their actual distance on the jar would be significantly farther apart in either scenario, but they're positioned as close as possible in these photos for the sake of comparison under the same lighting conditions).  These photos show what appears to be a raised band running above the jar's main curvature, with a smaller raised band in the bottom of the large band.  This would seem to be compelling evidence for a match; however, there's enough of a difference in the shape of the band to raise doubts about the handles belonging to the same jar.  The small, fragmentary nature of #36 hampers the investigation.

Therefore, the best explanation for all the other characteristics of similarity, is that these 2 handles belonged to 2 different jars that were made from the same batch of clay, formed by the same potter on the same day, stamped by the exact same seal-officer, fired in the same oven, & traveled together during the course of their usage since they ended up in the same unknown locus in antiquity, where they were found at some point in modern times.