There is currently no method of merging databases, sorry. Your only option would be to export the contents from database B to a single playlist on a USB drive, then bring that export drive to computer A and import the playlists and music files.
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I would move each data base to an external hard drive and then merge that drive to your new computer. I only use external drives, so I am able to move between computers easily, but may be the simplest way to achieve the move.
I will go two external hd too. I am interested in knowing how to merge between the two databases in RB.
Use usb fat32 stick or hd i prefer usb stick
Export one by one each playslist on the stick
after on the tree on your left go on device you should see all the playlist
one by one import in the hard disk containing your master database
junior