Cannot understand how changing at Fratton, would make the journey a lot quicker.
There are a couple of direct trains a day between Salisbury and Chichester - G W R service.
Travelling from Salisbury towards Portsmouth and changing at either Southampton Central, Fareham or Cosham onto a Southern service to Chichester makes the journey about 20 minutes shorter.
Journey planners will say change at Southampton but this could mean crossing platforms.
Stay on train and change at Fareham or Cosham does not involve changing platform.
Note some of the evening GWR services do not call at Cosham