i dont know how bad its doing it, is it at high speed or just turn in speed say 10mph or tat? gravel or tarmac? if its doing it at any speed and on tarmac i would put a guess on a gear box and rear diff conflict, ie the rear diff doesnt match the gear box,
the first diff that he replaced may have not been for the gearbox or more likely the gear box has been changed and the diffs are not matching it.. did the car ever drive right wen he had it or is this the way he bought it?? if always like this i would try an establish which box i had,. ie 5spd, 6spd, 6spd uk, 6spd japetc etc, and what year/ model ie sti/ wrx/ sti ra etc. there was a lot of different gear box and diff in classics so with his car is it the gear box or the dif that belongs in that car?? thats all i can think off