I have a suspicion of contextual inaccuracy. And I honestly have been searching “Trump”“declassified” “declassify” and “snopes” for an hour. Perhaps it was politifact or… hmm can’t think of the other… oh, yes! Fact-check.org you mean?
Either case, Snopes kept taking me to associates press reports, which were valid, and did indeed say the President has the authority but it doesn’t explicitly state that a verbal acknowledgement is enough, nor whether he had the authority to do so during the move, since by then, he may have been a former President at the time. Which, I’ll admit, is unlikely even if you were correct. I believe the packing and moving takes place well before Biden’s inauguration. So he may have certainly had the authority before taking the documents off the premises.
In fact, mistakingly taking documents off premises isn’t even a crime according to the Associated Press. It became criminal when he knowingly withheld them after his attorneys signed documents swearing all classified information has been removed from his personal residence(s).
Still, this article from fact-check.org appears to contradict your claim.
“The procedure is far more formal,” said Immerman, who is now a historian at Temple University. “Documents must be declassified page by page; in fact, if TS/SCI [Top Secret/Sensitive Compartmented Information] line by line. The document then is marked declassified (often sanitized) by the authorizing agent along with the date. Consequently, former President Trump’s claim is to me implausible.”
https://www.factcheck.org/2022/08/trumps-dubious-standing-order-to-declassify-documents/
Of course, Immerman may be in error.
By all means, tell me what you found on snopes as my searches haven’t found anything that confirms your claim.