I was recently tasked with migrating a user to a new user profile. This user was a VIP and was adamant about wanting her recently used file list inside of Acrobat Reader. I could find no documentation on how to move this information. I resorted to searching the Windows registry. It turns out the location is under HKEY_CURRENT_USER or HKEY_USERS (depending on if you are logged in as the user or not). The registry location is:
HKEY_USERS\[User's SID]\SOFTWARE\Adobe\Acrobat Reader\DC\AVGeneral\cRecentFiles
Under that key there will be folders like c1, c2, c3, c4, etc. each one of those is a file entry. You want to export the entire "cRecentFiles" key. Then import it to your new profile into the registry.
This brings up a good trick I use when trying to find things in the Windows registry. In this case I took a PDF file and renamed it to something I thought probably wouldn't exist anywhere else in the registry. Something IKEA.pdf for instance. Then I opened that PDF in Acrobat (hoping it would then be in my history - which it was). Then I opened regedit and searched for the word IKEA. It found the very location I'm telling you about. Easy as that.