Details of the convoy, including the Abby, when leaving Jamaica, are given in Royal Gazette of Jamaica – 22 Sep 1781
I have found that the Abby did successfully reach Lancaster which was its intended destination.
Lloyds List No, 1312 23 Nov 1781
Lancaster
arrived from Jamaica
Abby, Cort
https://babel.hathitrust.org/cgi/pt?id=mdp.39015004281559;skin=2021;sz=25;q1=abby%20cort;start=1;sort=seq;page=search;seq=200;num=1319
This removes any possibility that John Cort landed in Portsmouth even though not arriving with the Princess Royal .