If a work item is not completed, if it doesn't meet its definition of done, then its not done. Crediting your team with a portion of the story points is going back to old PM mindsets.
The correct thing to do is to bring it forward to the next sprint (as long as the PO still believes there is business value in completing the User Story). The aim of agile is to deliver business value, and there is no value in Stories 95% done and not implemented into a production environment.
Failing this there is a danger of having a backlog containing lots of nearly completed stories, and carrying these from sprint to sprint, clogging up your board. And worse, crediting your team with success for nearly completing them.
The best measure is done, 100% done, live and delivering value!
Good Luck with it !