Background information Edit
Though not fully described in the film or script, the term "Jaylah stick" was used to described the object, which comes from a sketch shown in the featurette "Properly Outfitted". (Star Trek Beyond - Collector's Edition special features) The same concept art named John Eaves as the tool's designer.
Mounting Jaylah's staff on Sofia Boutella's back without it bouncing around even when she had to remove it was, according to Star Trek Beyond Property Master Andrew M. Siegel, "always difficult." The film's creative team therefore created a blocking mechanism for the actress' back. ("Properly Outfitted", Star Trek Beyond - Collector's Edition special features) A pair of concept diagrams of the equipment on Jaylah's back can be seen at TrekCore.
After the team invented the blocking mechanism, the idea of increasing the tool's versatility came up. "We thought, 'Oh, she needs a rifle later,' so rather than give her some unmotivated thing," recalled Andy Seigel, "we went, 'Oh, okay, what if she just takes her staff, and we take pieces off and add pieces to it?'" ("Properly Outfitted", Star Trek Beyond - Collector's Edition special features)
After its on-screen usage was finished but before the release of Star Trek Beyond, the stunt prop of Jaylah's staff was won – at a celebratory fan event held at the Paramount Pictures lot on 16 May 2016 – by Doyle Zhang, who had flown from Shanghai to attend the event. (Star Trek Magazine Movie Special 2016, p. 94)