We don't know exactly how they're archiving his tweets, but it's the first confirmation that even his retracted and typo-filled messages will be saved. But concerns to save them came soon after it was clear Trump would continue his feverish Twitter posting. Back in February, Tom Carper (DE) and Claire McCaskill (MO) sent a letter to Secretary of Defense James Mattis asking after the security of Trump's unsecured Android smartphone (which he only replaced last week).
David S. Ferriero, head of the National Archives and Records Administration (NARA), replied to the pair and assured them Trump's Twitter messages would be saved. The White House had acquiesced to Ferriero's requests to save the President's current and future tweets, including ones that were deleted.
NARA was formed after the Nixon administration to make public the archives of Presidential correspondence. It's the kind of safeguard that was supposed to protect against things like the George W. Bush administration "losing" 22 million emails between 2003 and 2009. In the event that the Trump team permits a similarly obscene level of erasure of public documents, at least ProPublica is looking after his deleted tweets, which they've tracked back to June 2015.