Sopot = Brighton
Lodz = Birmingham
Got to go with Leeds here both cities had big textile industries also large Jewish communities, Leeds has the second largest Jewish community in the UK outside of North London.
Gdansk = Liverpool
Belfast may be a more interesting twin with Gdansk the Titanic was built in Belfast and it was a world leader at one stage. Liverpool was more of a delivery port.
What would Poznan be?
I would put Birmingham as Poznan's twin city, it's close to the west although it is rooted in the east. More seriously "Concordia Design", "Poznan School of Form", "Art&Fashion Festival" to mention only a few. Poznan is also becoming a know-how hub with many technological parks and transfer of knowledge centers (the oldest one started in 1995 is "Poznan Science and Technology Park".The city hosts regular international trade fairs and was the host city for the United Nations Climate Change Conference.