Yes it's valid via Portsmouth (Both Stations) and Valid for BOJ on Outward and Return Portions.
Is it?
I wasn't aware of an easement that allowes double backing through Fratton.
They are all part of Portsmouth Group.
Customers travelling between Chichester and Cosham may double back between Hilsea and Fratton. This easement applies in both directions.
Cosham is a member of Portsmouth Group so if your ticket is Cosham - Chichester then you're not permitted otherwise without the easement to double-back within Portsmouth Group as it is the origin.
So positive double-back easement. You're not allowed to double-back any further.