How did you created the local copy may be the clue for the solution.
If you go to File > Open and select c:\wrk\a.slddrw (but don't open it yet), then you can click the References button and it will show the references. If \\srv\root\a.sldprt shows up there then you can double click on it and point to c:\wrk\a.sldprt instead. Then click open and the reference should be updated to the local version. Just make sure you save it after that.