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When Alex receives the order to assassinate the Mako weapons maker who invented the Mag Rail schematics, who gave this order to Lin May Chen? The Illuminati or the Templar insurgents? (Also begs the question when was Saman inducted as a Templar, & who inducted him... Everett, or an enemy of MJ12 & the Illuminati?)
Chen received orders from one of them. I speculate it was whoever was working with she and Billie at the time. Her Holiness did not give the order, so it was likely a Templar sanctioned contract just like the Mag Rail private mass production. The WTO wanted Alex to pick up the gun in order to read its Nano imprint through their access thru Alex's infolink broadcast sense-data. They would be able to take the spec from there & develop their own mass production of the Mag Rail on their 3D Printers/Nanoformers.
However, if Alex kills the Project Lead, who likely has the schematics in his datalogs, and the gun itself becomes only available to Templars, then it would be quite inaccessible to anyone in the WTO or the Illuminati unless they either took it from a Templar casualty or infiltrator (they may have access to Billie's infolink sense-data, but strategically Billie never uses a Mag Rail).
My theory: Lin May Chen received the order to kill the Project Lead under the guise of some cultist fanatical sanctimony (terrorism). The Zealotry was ostensibly for glory & what Chad Dumier calls "the communication event", but the real purpose of this was to stop the Illuminati from obtaining the schematics from the unlicensed private Mag Rail project and contract commissioned by the Templars who have somehow regained their gold stockpile (from Everett or the MJ12, or the Vatican).