Either pickpocket or shoot the fusion core (you can target it in VATS), while the owner is still alive. This will eject the baddie so you can nab the frame, too. However, it will be marked as stolen, and some npcs may give you grief for that.

Note: I am in no way defending either the letter writer or the responder from Uexpress. I think we can all agree they are both shitty people.