Migrating DAM to FAL during an update of TYPO3 4.5 to 6.2 could be a little bit tricky, but for the migrating of DAM to FAL is used the extension we_dam2fal62 and had a successfull migration of all the tt_content data and was very happy.
After following the manual of the extension, the migrating was very easy.
But when checking the complete page, I found out, that all the media files in tt_news records weren't updated to FAL because it seems not to be implemented in this extension.
After a short research, I couldn't find a smart solution to convert the bodytext data records in tt_news records.
Because of that I built a little backend extension which converts all the <media> entries in tt_news records to the new <link> element and references to FAL, called reint_ttnewsdamtofal.
The extension only needs the old tx_dam table to find the old DAM records.
Find out and send me feedback, I hope this helps other people, too!