After Twitter migrated to the retarded x domain name (if you had an account, you were forcibly moved in the past week), it is now once again possible to archive tweets with Archive.today - archive.org still fails, unfortunately.
Obviously, you have to select the x domain name though.
Oh hell no, I'm not even sure they were aware of it.
Which is a bloody shame, because as someone who is critical of the lying media, Elon should love the archiving stuff.