This page is dated March 2014, so I have no idea whether the single seat listed is current, but on a static page, or whether the whole page itself is stale:
https://www.brightonandhovealbion.com/news/2014/march/private-seat-licenses/
Indeed it does, and I knew that bit.
But I couldn't recall whether the PSL comes with built-in match-by-match transferability. I've found nothing to suggest it does.