I know how the Engineers might have spun the Ring (Score 1)

In 'Ringworld Engineers' you say that it would have taken the energy from 12 gas giants to spin the Ringworld up to speed. In one of your Known Space stories (I forget which)you say that teleported objects in Known Space retain their momentum. You also say there is no distance limit on teleporting. Isn't it therefore possible that the Engineers could have teleported matter from a system with a relative velocity differential approaching c. Wouldn't such a setup give them all the energy they could ever possibly want?