Who writes acceptance criteria?. Should you even have acceptance criteria? It's a loaded question, because it's assuming that we're using user stories. And in user stories typically you might say in order to deliver a particular type of value, some particular persona wants or needs something in order to do so, and then you typically list off your acceptance criteria.
These are the things that if they were in place, I would be happy with it. And then you might have some non-functional acceptance criteria. It needs to comply with a particular international standard, or it needs to perform it in a particular period of time. Acceptance criteria are very useful because when the team is working on the work item, they have a sense of what work they need to do to help to deliver that.
You shouldn’t be handing work anywhere, you should be collaborating, but you just work together and try to understand that together. And that’s what we expect in scrum. We expect you to collaborate and not run onto your next thing. There are no roles in scrum. We do have accountabilities, but you don’t have like sub roles if you like.