How are you supposed to prove the tweet actually happened if you just post a screenshot? It's trivial to forge a screenshot of a tweet to say whatever you want.
It's presumably trivial to forge Twitter's "verified" embedding as well, so that doesn't prove anything. (Just have it link to a deleted tweet - plausible deniability!)
If it still exists, just add a link to it underneath the screenshot. If it was deleted, then there's not much you can do, but that's no different than if you had embedded it.