Yes, once the President leaves office, he is obliged to hand over classified documents to the archives. Other documents typically go to his Presidential library. Typically X-Presidents (mainly his staff) are charged with the process of transferring these documents. Separating the classified ones takes some time and all Presidents do this. Trump asked if he could transfer boxes of documents to Mar-A-Lago and was told yes. Soon after, government officials inspected the storage area and told Trump to put an extra lock on the storage area which he did. Shortly after that the FBI raided Mar-A-Lago and claimed to find classified documents there. Normally this would be an issue settled with archives because it's not a crime. Trump let them go through the boxes the first time and cooperated and, as I said, right after that, the FBI raided the same place and also went through Trump's personal spaces like his closets, desks, etc. This is nothing but a desperate, tyrannical Biden administration attempt at trying to find crimes to lock up his political opponent.
A shorter answer: A President can classify and declassify right up to the point of his leaving office. After that the X-President and archives typically work together to decide on where the documents will go. It was NEVER considered a crime to misplace documents due to filing errors. Even if Trump had classified documents, WTF was he going to do with them? Give them to Putin?