They would go to the Division Head for the division housing the division—in this case research, so Thranduil! Who can assign things to whomever he sees fit.

And their specific orders would be to see whether rifter phylacteries can be created, test them as locators and remote casting tools, and otherwise figure out if there are any unforeseen consequences or difficulties. The other stuff we mentioned is just bonus stuff that would be cool to know/relevant to the project's larger mission and possibly fun to RP.